Exam 9: Matrices and Determinants

Add and Subtract Matrices -Let $\mathrm { A } = \left[ \begin{array} { r r r } 2 & 4 & 1 \\ 4 & 2 & - 1 \\ - 1 & 2 & 3 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { r r r } 3 & - 4 & 1 \\ - 1 & 0 & 2 \\ 0 & 3 & - 2 \end{array} \right]$ . Find $\mathrm { A } + \mathrm { B }$ .

Multiplicative Inverses of Matrices and Matrix Equations 1 Find the Multiplicative Inverse of a Square Matrix - $\mathrm { A } = \left[ \begin{array} { r r } - 1 & 0 \\ 4 & 2 \end{array} \right]$

Multiply Matrices - $A=\left[\begin{array}{r}-5-8-6 \\8-3-6\end{array}\right], B=\left[\begin{array}{r}-2 \\3 \\9\end{array}\right]$

Solve a System of Linear Equations in Three Variables Using Cramer's Rule - -2x-2y-z=-13 x+6y+6z=43 6x+y+z=13

Inconsistent and Dependent Systems and Their Applications 1 Apply Gaussian Elimination to Systems Without Unique Solutions - 5x+2y+z =-11 2x-3y-z =17 7x-y =12

Use Determinants to Identify Inconsistent Systems and Systems with Dependent Equations - x+z=1 2x-2y=-2 y+z=4

Write the matrix equation as a system of linear equations without matrices. - $\left[ \begin{array} { l l l } 3 & 2 & 8 \\9 & 0 & 7 \\4 & 9 & 0\end{array} \right] \left[ \begin{array} { l } x \\y \\z\end{array} \right] = \left[ \begin{array} { r } - 2 \\4 \\2\end{array} \right]$

Solve a System of Linear Equations in Two Variables Using Cramer's Rule - 3x=55-4y 3y=48-3x

Write the matrix equation as a system of linear equations without matrices. - $\left[ \begin{array} { r r } 4 & 19 \\ 10 & 20 \end{array} \right] \left[ \begin{array} { l } x \\ y \end{array} \right] = \left[ \begin{array} { l } 3 \\ 3 \end{array} \right]$

Solve the problem using matrices. -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. $\left. \begin{array} { l c c } & \text { Midterm } & \text { Final } \\\text { Student 1 } & 73 & 79 \\\text { Student 2 } & 44 & 62 \\\text { Student 3 } & 81 & 85 \\\text { Student 4 } & 98 & 96\end{array} \right]$ Find the final course score for Student 3 for both grading System 1 and System 2.

Simplify Complex Rational Expressions - 9x+5z=65 3y+6z=27 2x+8y+6z=42

Apply Gaussian Elimination to Systems with More Variables than Equations - 2x+y+2z-4w =10 x+3y+2z-11w =17 3x+y+7z-21w =0

Model Applied Situations with Matrix Operations -Adjust the contrast by leaving the black alone and changing the light grey to dark grey. Use matrix addition to accomplish this.

Use Matrices and Gauss-Jordan Elimination to Solve Systems - x=-1-y-z x-y+4z=-6 3x+y=7-z

Inconsistent and Dependent Systems and Their Applications 1 Apply Gaussian Elimination to Systems Without Unique Solutions - x+y+z =9 2x-3y+4z =7 x-4y+3z =-2

Solve Matrix Equations -Let $\mathrm { A } = \left[ \begin{array} { r r } 7 & - 7 \\ - 4 & 0 \\ 10 & - 1 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { r r } 10 & 0 \\ 0 & - 2 \\ 7 & - 1 \end{array} \right] ; \quad 4 X + A = B$

Evaluate Higher-Order Determinants - $\left| \begin{array} { l l l l } 0 & 0 & 0 & 8 \\4 & 6 & 9 & 5 \\9 & 8 & 7 & 3 \\3 & 3 & 1 & 7\end{array} \right|$

Understand What is Meant by Equal Matrices - $\left[ \begin{array} { r r } x & y + 6 \\9 z & 3\end{array} \right] = \left[ \begin{array} { c c } 8 & 8 \\90 & 3\end{array} \right]$

Solve a System of Linear Equations in Two Variables Using Cramer's Rule - 7x+8y=4 2x+3y=2

Inconsistent and Dependent Systems and Their Applications 1 Apply Gaussian Elimination to Systems Without Unique Solutions - 3x-2y+2z-w=2 4x+y+z+6w=8 -3x+2y-2z+w=5 5x+3z-2w=1