Matrix A is given. Find appropriate identity matrices IS1U1B1mS1U1B0 and IS1U1B1nS1U1B0 such that IS1U1B1mS1U1B0A = A and AIS1U1B1nS1U1B0 = A. -\[A = \left[ \begin{array} { r r r } 3 & 0 & - 8 \\ 1 & 8 & - 8 \\ - 1 & - 1 & - 2 \end{array} \right]\]

A) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right]$ B) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]$ C) $\mathrm { I } _ { \mathrm { m } } = \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]$ D) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]$ A) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right]$ B) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]$ C) $\mathrm { I } _ { \mathrm { m } } = \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]$ D) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]$

Matrix A is given. Find appropriate identity matrices IS1U1B1mS1U1B0 and IS1U1B1nS1U1B0 such that IS1U1B1mS1U1B0A = A and AIS1U1B1nS1U1B0 = A. -\[A = \left[ \begin{array} { r r } 2 & - 7 \\ 6 & 0 \\ - 6 & 9 \\ 7 & - 2 \end{array} \right]\]

A) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right]$ B) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right]$ C) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right]$ D) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]$ A) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right]$ B) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right]$ C) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right]$ D) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]$

Calculate $| \mathbf { A } |$ -\[\begin{aligned} 9 x - 9 y - z & = - 30 \\ x - 5 y - 6 z & = - 41 \\ - 8 x + y + z & = - 8 \end{aligned}\]

A) $( 3,3,3 )$ B) $( 2 , - 5 , - 3 )$ C) $( 2,5,3 )$ D) $( 5,3,5 )$ A) $( 3,3,3 )$ B) $( 2 , - 5 , - 3 )$ C) $( 2,5,3 )$ D) $( 5,3,5 )$

Matrix A is given. Find appropriate identity matrices IS1U1B1mS1U1B0 and IS1U1B1nS1U1B0 such that IS1U1B1mS1U1B0A = A and AIS1U1B1nS1U1B0 = A. -\[A = \left[ \begin{array} { r r r r } 3 & 0 & 1 & 5 \\ - 4 & 9 & - 1 & 7 \end{array} \right]\]

A) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]$ B) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right]$ C) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right]$ D) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 1 \\ 1 & 1 \end{array} \right]$ A) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right]$ B) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right]$ C) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right]$ D) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 1 \\ 1 & 1 \end{array} \right]$

Exam 8: Matrices

Matrix A is given. Find appropriate identity matrices I_m and I_n such that I_mA = A and AI_n = A. - $A = \left[ \begin{array} { r r r } 3 & 0 & - 8 \\1 & 8 & - 8 \\- 1 & - 1 & - 2\end{array} \right]$

(Multiple Choice)

Matrix A is given. Find appropriate identity matrices I_m and I_n such that I_mA = A and AI_n = A. - $A = \left[ \begin{array} { r r r } 3 & 0 & - 8 \\1 & 8 & - 8 \\- 1 & - 1 & - 2\end{array} \right]$

Determine whether matrix B is the inverse of matrix A by finding the product AB. - $A = \left[ \begin{array} { r r } - 2 & 4 \\ 4 & - 4 \end{array} \right] , B = \left[ \begin{array} { l l } \frac { 1 } { 2 } & \frac { 1 } { 4 } \\ \frac { 1 } { 2 } & \frac { 1 } { 4 } \end{array} \right]$

Determine the size of matrix A and tell whether it is a square matrix, row matrix, column matrix, or none of these. - $A = \left[ \begin{array} { r r r r } \sqrt { 3 } & - 7 & 1 & 6 \\\pi & 8 & - 1 & 4\end{array} \right]$

Determine whether matrix B is the inverse of matrix A by finding the product AB. - $A = \left[ \begin{array} { c c } 10 & 1 \\- 1 & 0\end{array} \right] , B = \left[ \begin{array} { r r } 0 & 1 \\- 1 & 10\end{array} \right]$

Find the indicated matrix. -Let $A = \left[ \begin{array} { r r } - 1 & 3 \\ 0 & 4 \\ 8 & - 4 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 7 & 2 \\ 17 & 4 \\ 3 & 2 \end{array} \right]$ . Find $A - B$

Find the inverse of the invertible matrix. - $\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 3 \\2 & 7 & 8\end{array} \right]$

Find the inverse of the invertible matrix. - $\left[ \begin{array} { r r r } 3 & - 3 & 1 \\- 2 & 2 & - 1 \\- 4 & 5 & - 2\end{array} \right]$

Find the inverse of the invertible matrix. - $\left[ \begin{array} { c c } 5 & 5 \\- 5 & 0\end{array} \right]$

Matrix A is given. Find appropriate identity matrices I_m and I_n such that I_mA = A and AI_n = A. - $A = \left[ \begin{array} { r r } 2 & - 7 \\6 & 0 \\- 6 & 9 \\7 & - 2\end{array} \right]$

Find the indicated matrix. -Let $\mathrm { A } = \left[ \begin{array} { r r } - 3 & 4 \\ 0 & 2 \end{array} \right]$ . Find $4 \mathrm {~A}$ .

Find the indicated matrix. -Let $A = \left[ \begin{array} { r r r } 4 & - 8 & 3 \\ 4 & 2 & - 2 \\ 8 & 1 & - 2 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } 1 & - 5 & 2 \\ - 8 & 1 & - 3 \\ 4 & - 5 & - 2 \end{array} \right]$ . Find 2A-3B.

Determine whether matrix B is the inverse of matrix A by finding the product AB. - $A = \left[ \begin{array} { r r r } 2 & - 1 & 0 \\- 1 & 1 & - 2 \\1 & 0 & - 1\end{array} \right] , B = \left[ \begin{array} { r r r } 1 & - 1 & 2 \\- 3 & - 2 & 4 \\- 1 & 1 & 1\end{array} \right]$

Find the inverse of the invertible matrix. - $\left[ \begin{array} { l l l } 1 & 0 & 8 \\ 1 & 2 & 3 \\ 2 & 5 & 3 \end{array} \right]$

Calculate $| \mathbf { A } |$ - $A = \left| \begin{array} { r r r } 1 & 1 & 4 \\2 & - 2 & 1 \\- 1 & - 4 & 1\end{array} \right|$

Solve the problem. -The final grade for an algebra course is determined by grades on the midterm and final exam. The grades for four students and two possible grading systems are modeled by the following matrices. Find the final course score for Student 3 for both grading System 1 and System 2.

Find the inverse of the invertible matrix. - $\left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]$

Calculate $| \mathbf { A } |$ - $A = \left| \begin{array} { r r r } - 1 & 4 & 2 \\- 2 & - 2 & 5 \\- 3 & - 3 & - 3\end{array} \right|$

Calculate $| \mathbf { A } |$ - 9x-9y-z =-30 x-5y-6z =-41 -8x+y+z =-8

Matrix A is given. Find appropriate identity matrices I_m and I_n such that I_mA = A and AI_n = A. - $A = \left[ \begin{array} { r r r r } 3 & 0 & 1 & 5 \\- 4 & 9 & - 1 & 7\end{array} \right]$

Calculate $| \mathbf { A } |$ - $A = \left| \begin{array} { l l l } 1 & 2 & 3 \\2 & 5 & 5 \\1 & 2 & 3\end{array} \right|$

Equations, Inequalities, and Applications

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Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

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Exam 8: Matrices

Matrix A is given. Find appropriate identity matrices Im and In such that ImA = A and AIn = A. - A=[30−818−8−1−1−2]A = \left[ \begin{array} { r r r } 3 & 0 & - 8 \\1 & 8 & - 8 \\- 1 & - 1 & - 2\end{array} \right]A=​31−1​08−1​−8−8−2​​

Determine the size of matrix A and tell whether it is a square matrix, row matrix, column matrix, or none of these. - A=[3−716π8−14]A = \left[ \begin{array} { r r r r } \sqrt { 3 } & - 7 & 1 & 6 \\\pi & 8 & - 1 & 4\end{array} \right]A=[3​π​−78​1−1​64​]

Determine whether matrix B is the inverse of matrix A by finding the product AB. - A=[101−10],B=[01−110]A = \left[ \begin{array} { c c } 10 & 1 \\- 1 & 0\end{array} \right] , B = \left[ \begin{array} { r r } 0 & 1 \\- 1 & 10\end{array} \right]A=[10−1​10​],B=[0−1​110​]

Find the indicated matrix. -Let A=[−13048−4]A = \left[ \begin{array} { r r } - 1 & 3 \\ 0 & 4 \\ 8 & - 4 \end{array} \right]A=​−108​34−4​​ and B=[7217432]B = \left[ \begin{array} { r r } 7 & 2 \\ 17 & 4 \\ 3 & 2 \end{array} \right]B=​7173​242​​ . Find A−BA - BA−B

Find the inverse of the invertible matrix. - [132133278]\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 3 \\2 & 7 & 8\end{array} \right]​112​337​238​​

Find the inverse of the invertible matrix. - [3−31−22−1−45−2]\left[ \begin{array} { r r r } 3 & - 3 & 1 \\- 2 & 2 & - 1 \\- 4 & 5 & - 2\end{array} \right]​3−2−4​−325​1−1−2​​

Find the inverse of the invertible matrix. - [55−50]\left[ \begin{array} { c c } 5 & 5 \\- 5 & 0\end{array} \right][5−5​50​]

Matrix A is given. Find appropriate identity matrices Im and In such that ImA = A and AIn = A. - A=[2−760−697−2]A = \left[ \begin{array} { r r } 2 & - 7 \\6 & 0 \\- 6 & 9 \\7 & - 2\end{array} \right]A=​26−67​−709−2​​

Find the indicated matrix. -Let A=[−3402]\mathrm { A } = \left[ \begin{array} { r r } - 3 & 4 \\ 0 & 2 \end{array} \right]A=[−30​42​] . Find 4 A4 \mathrm {~A}4 A .

Find the inverse of the invertible matrix. - [108123253]\left[ \begin{array} { l l l } 1 & 0 & 8 \\ 1 & 2 & 3 \\ 2 & 5 & 3 \end{array} \right]​112​025​833​​

Calculate ∣A∣| \mathbf { A } |∣A∣ - A=∣1142−21−1−41∣A = \left| \begin{array} { r r r } 1 & 1 & 4 \\2 & - 2 & 1 \\- 1 & - 4 & 1\end{array} \right|A=​12−1​1−2−4​411​​

Solve the problem. -The final grade for an algebra course is determined by grades on the midterm and final exam. The grades for four students and two possible grading systems are modeled by the following matrices. Find the final course score for Student 3 for both grading System 1 and System 2.

Find the inverse of the invertible matrix. - [111211223]\left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]​122​112​113​​

Calculate ∣A∣| \mathbf { A } |∣A∣ - A=∣−142−2−25−3−3−3∣A = \left| \begin{array} { r r r } - 1 & 4 & 2 \\- 2 & - 2 & 5 \\- 3 & - 3 & - 3\end{array} \right|A=​−1−2−3​4−2−3​25−3​​

Calculate ∣A∣| \mathbf { A } |∣A∣ - 9x-9y-z =-30 x-5y-6z =-41 -8x+y+z =-8

Matrix A is given. Find appropriate identity matrices Im and In such that ImA = A and AIn = A. - A=[3015−49−17]A = \left[ \begin{array} { r r r r } 3 & 0 & 1 & 5 \\- 4 & 9 & - 1 & 7\end{array} \right]A=[3−4​09​1−1​57​]

Calculate ∣A∣| \mathbf { A } |∣A∣ - A=∣123255123∣A = \left| \begin{array} { l l l } 1 & 2 & 3 \\2 & 5 & 5 \\1 & 2 & 3\end{array} \right|A=​121​252​353​​

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Matrix A is given. Find appropriate identity matrices I_m and I_n such that I_mA = A and AI_n = A. - $A = \left[ \begin{array} { r r r } 3 & 0 & - 8 \\1 & 8 & - 8 \\- 1 & - 1 & - 2\end{array} \right]$

Determine the size of matrix A and tell whether it is a square matrix, row matrix, column matrix, or none of these. - $A = \left[ \begin{array} { r r r r } \sqrt { 3 } & - 7 & 1 & 6 \\\pi & 8 & - 1 & 4\end{array} \right]$

Determine whether matrix B is the inverse of matrix A by finding the product AB. - $A = \left[ \begin{array} { c c } 10 & 1 \\- 1 & 0\end{array} \right] , B = \left[ \begin{array} { r r } 0 & 1 \\- 1 & 10\end{array} \right]$

Find the indicated matrix. -Let $A = \left[ \begin{array} { r r } - 1 & 3 \\ 0 & 4 \\ 8 & - 4 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 7 & 2 \\ 17 & 4 \\ 3 & 2 \end{array} \right]$ . Find $A - B$

Find the inverse of the invertible matrix. - $\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 3 \\2 & 7 & 8\end{array} \right]$

Find the inverse of the invertible matrix. - $\left[ \begin{array} { r r r } 3 & - 3 & 1 \\- 2 & 2 & - 1 \\- 4 & 5 & - 2\end{array} \right]$

Find the inverse of the invertible matrix. - $\left[ \begin{array} { c c } 5 & 5 \\- 5 & 0\end{array} \right]$

Matrix A is given. Find appropriate identity matrices I_m and I_n such that I_mA = A and AI_n = A. - $A = \left[ \begin{array} { r r } 2 & - 7 \\6 & 0 \\- 6 & 9 \\7 & - 2\end{array} \right]$

Find the indicated matrix. -Let $\mathrm { A } = \left[ \begin{array} { r r } - 3 & 4 \\ 0 & 2 \end{array} \right]$ . Find $4 \mathrm {~A}$ .

Find the inverse of the invertible matrix. - $\left[ \begin{array} { l l l } 1 & 0 & 8 \\ 1 & 2 & 3 \\ 2 & 5 & 3 \end{array} \right]$

Calculate $| \mathbf { A } |$ - $A = \left| \begin{array} { r r r } 1 & 1 & 4 \\2 & - 2 & 1 \\- 1 & - 4 & 1\end{array} \right|$

Find the inverse of the invertible matrix. - $\left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]$

Calculate $| \mathbf { A } |$ - $A = \left| \begin{array} { r r r } - 1 & 4 & 2 \\- 2 & - 2 & 5 \\- 3 & - 3 & - 3\end{array} \right|$

Calculate $| \mathbf { A } |$ - 9x-9y-z =-30 x-5y-6z =-41 -8x+y+z =-8

Matrix A is given. Find appropriate identity matrices I_m and I_n such that I_mA = A and AI_n = A. - $A = \left[ \begin{array} { r r r r } 3 & 0 & 1 & 5 \\- 4 & 9 & - 1 & 7\end{array} \right]$

Calculate $| \mathbf { A } |$ - $A = \left| \begin{array} { l l l } 1 & 2 & 3 \\2 & 5 & 5 \\1 & 2 & 3\end{array} \right|$