Write the augmented matrix for the system. Do not -\[\begin{array} { l } 9 x + 6 y = - 3 \\ 5 x + 2 y = 1 \end{array}\]

A) \[\left[ \begin{array} { r r | r } 9 & 6 & - 3 \\ 5 & 2 & 1 \end{array} \right]\] B) \[\left[ \begin{array} { r r | r } - 3 & 6 & 9 \\ 1 & 5 & 2 \end{array} \right]\] C) \[\left[ \begin{array} { r r | r } 9 & 6 & 1 \\ 2 & 5 & - 3 \end{array} \right]\] D) \[\left[ \begin{array} { r r | r } 9 & 5 & - 3 \\ 6 & 2 & 1 \end{array} \right]\] A) \[\left[ \begin{array} { r r | r } 9 & 6 & - 3 \\ 5 & 2 & 1 \end{array} \right]\] B) \[\left[ \begin{array} { r r | r } - 3 & 6 & 9 \\ 1 & 5 & 2 \end{array} \right]\] C) \[\left[ \begin{array} { r r | r } 9 & 6 & 1 \\ 2 & 5 & - 3 \end{array} \right]\] D) \[\left[ \begin{array} { r r | r } 9 & 5 & - 3 \\ 6 & 2 & 1 \end{array} \right]\]

Solve the system by substitution. -\[\begin{array} { r } x + 8 y = 35 \\ 2 x + 8 y = 30 \end{array}\]

A) $\{ ( 5,4 ) \}$ B) $\{ ( - 4 , - 5 ) \}$ C) $\{ ( - 5,5 ) \}$ D) $\varnothing$ A) $\{ ( 5,4 ) \}$ B) $\{ ( - 4 , - 5 ) \}$ C) $\{ ( - 5,5 ) \}$ D) $\varnothing$

Exam 10: Systems and Matrices

Provide an appropriate response. -Let $A = \left[ \begin{array} { r r } - 4 & - 4 \\ - 6 & 3 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 1 & 4 \\ 5 & - 3 \end{array} \right]$ Does the matrix $A + B$ have an inverse?

(Multiple Choice)

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Question 181

Solve the equation for x. - $\left| \begin{array} { l l } x & 3 \\2 & 1\end{array} \right| = 6$

(Multiple Choice)

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Question 182

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

(Multiple Choice)

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Question 183

Write the augmented matrix for the system. Do not - 9x+6y=-3 5x+2y=1

(Multiple Choice)

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Question 184

Solve the system to find $W _ { 1 } \text { and } W _ { 2 }$ -Linear systems occur in the design of roof trusses for new homes and buildings. The simplest type 223) of roof truss is a triangle. The truss shown in the figure is used to frame roofs of small buildings. If A force of 116 pounds is applied at the peak of the truss, then the forces or weight $\mathrm { W } _ { 1 } \text { and } \mathrm { W } _ { 2 }$ exerted parallel to each rafter of the truss are determined by the following linear system of equations. $Solve the system to find W _ { 1 } \text { and } W _ { 2 } -Linear systems occur in the design of roof trusses for new homes and buildings. The simplest type 223) of roof truss is a triangle. The truss shown in the figure is used to frame roofs of small buildings. If A force of 116 pounds is applied at the peak of the truss, then the forces or weight \mathrm { W } _ { 1 } \text { and } \mathrm { W } _ { 2 } exerted parallel to each rafter of the truss are determined by the following linear system of equations. \begin{array} { l } \frac { \sqrt { 3 } } { 2 } \left( W _ { 1 } + W _ { 2 } \right) = 116 \\ W _ { 1 } - W _ { 2 } = 0 \end{array}$ + =116 -=0

(Multiple Choice)

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Question 185

Use a graphing calcula tor to find the inverse of the matrix. Give five decimal places, if necessary. - $A = \left[ \begin{array} { c c } \frac { 4 } { 3 } & 52 \\\sqrt { 21 } & 8.754\end{array} \right]$

(Multiple Choice)

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Question 186

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - +=80 -=48

(Multiple Choice)

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Question 187

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r r } 6 & - 3 & 4 & - 3 \\6 & - 2 & - 3 & - 2 \\12 & - 5 & 1 & - 5 \\0 & - 6 & 8 & 0\end{array} \right]$

(Multiple Choice)

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Question 188

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - 2x-y-5z=-14 -2x+4y+4z=16 -8x-4y+z=-36

(Multiple Choice)

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Question 189

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. - 3x+y=10 9x+4y=25

(Multiple Choice)

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Question 190

Solve the system to find $W _ { 1 } \text { and } W _ { 2 }$ -Linear systems occur in the design of roof trusses for new homes and buildings. The simplest type of roof truss is a triangle. The truss shown in the figure is used to frame roofs of small buildings. If A 172-pound force is applied at the peak of the truss, then the forces or weights W $\mathrm { W } _ { 1 } \text { and } \mathrm { W } _ { 2 }$ exerted Parallel to each rafter of the truss are determined by the following linear system of equations. $Solve the system to find W _ { 1 } \text { and } W _ { 2 } -Linear systems occur in the design of roof trusses for new homes and buildings. The simplest type of roof truss is a triangle. The truss shown in the figure is used to frame roofs of small buildings. If A 172-pound force is applied at the peak of the truss, then the forces or weights W \mathrm { W } _ { 1 } \text { and } \mathrm { W } _ { 2 } exerted Parallel to each rafter of the truss are determined by the following linear system of equations. \begin{array}{l} W_{1}+\sqrt{2} W_{2}=344 \\ \sqrt{3} W_{1}-\sqrt{2} W_{2}=0 \end{array}$ +=344 -=0

(Multiple Choice)

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Question 191

Solve the equation for x. - $\left| \begin{array} { l l } x & 1 \\2 & x\end{array} \right| = - 1$

(Multiple Choice)

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Question 192

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - y=|x| 4x-y=-20

(Multiple Choice)

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Question 193

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - 1.2x+y=-8 -4.5x-y=10

(Multiple Choice)

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Question 194

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. -A is $2 \times 2$ ; B is $2 \times 2$ .

(Multiple Choice)

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Question 195

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } \leq 9$ $Which method should be used to solve the system? Explain your answer, including a description of the first step. - ( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } \leq 9$

(Multiple Choice)

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Question 196

Find the matrix product when possible. - $\left[ \begin{array} { r r } 3 & - 1 \\6 & 0\end{array} \right] \left[ \begin{array} { r r } 0 & - 1 \\2 & 6\end{array} \right]$

(Multiple Choice)

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Question 197

Provide an appropriate response. -Fill in the blank to complete the statement. Each number in a matrix is called of the matrix.

(Multiple Choice)

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Question 198

Solve the system by substitution. - x+8y=35 2x+8y=30

(Multiple Choice)

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Question 199

Solve the equation for x. - $\left| \begin{array} { l l l } x & 0 & 0 \\5 & x & 1 \\3 & 2 & 1\end{array} \right| = - 1$

(Multiple Choice)

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Question 200

Showing 181 - 200 of 507

Provide an appropriate response. -Let $A = \left[ \begin{array} { r r } - 4 & - 4 \\ - 6 & 3 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 1 & 4 \\ 5 & - 3 \end{array} \right]$ Does the matrix $A + B$ have an inverse?

Solve the equation for x. - $\left| \begin{array} { l l } x & 3 \\2 & 1\end{array} \right| = 6$

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Write the augmented matrix for the system. Do not - 9x+6y=-3 5x+2y=1

Use a graphing calcula tor to find the inverse of the matrix. Give five decimal places, if necessary. - $A = \left[ \begin{array} { c c } \frac { 4 } { 3 } & 52 \\\sqrt { 21 } & 8.754\end{array} \right]$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - +=80 -=48

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r r } 6 & - 3 & 4 & - 3 \\6 & - 2 & - 3 & - 2 \\12 & - 5 & 1 & - 5 \\0 & - 6 & 8 & 0\end{array} \right]$

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - 2x-y-5z=-14 -2x+4y+4z=16 -8x-4y+z=-36

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. - 3x+y=10 9x+4y=25

Solve the equation for x. - $\left| \begin{array} { l l } x & 1 \\2 & x\end{array} \right| = - 1$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - y=|x| 4x-y=-20

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - 1.2x+y=-8 -4.5x-y=10

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. -A is $2 \times 2$ ; B is $2 \times 2$ .

Find the matrix product when possible. - $\left[ \begin{array} { r r } 3 & - 1 \\6 & 0\end{array} \right] \left[ \begin{array} { r r } 0 & - 1 \\2 & 6\end{array} \right]$

Provide an appropriate response. -Fill in the blank to complete the statement. Each number in a matrix is called of the matrix.

Solve the system by substitution. - x+8y=35 2x+8y=30

Solve the equation for x. - $\left| \begin{array} { l l l } x & 0 & 0 \\5 & x & 1 \\3 & 2 & 1\end{array} \right| = - 1$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Filters

Exam 10: Systems and Matrices

Provide an appropriate response. -Let A=[−4−4−63]A = \left[ \begin{array} { r r } - 4 & - 4 \\ - 6 & 3 \end{array} \right]A=[−4−6​−43​] and B=[145−3]B = \left[ \begin{array} { r r } 1 & 4 \\ 5 & - 3 \end{array} \right]B=[15​4−3​] Does the matrix A+BA + BA+B have an inverse?

Solve the equation for x. - ∣x321∣=6\left| \begin{array} { l l } x & 3 \\2 & 1\end{array} \right| = 6​x2​31​​=6

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Write the augmented matrix for the system. Do not - 9x+6y=-3 5x+2y=1

Use a graphing calcula tor to find the inverse of the matrix. Give five decimal places, if necessary. - A=[4352218.754]A = \left[ \begin{array} { c c } \frac { 4 } { 3 } & 52 \\\sqrt { 21 } & 8.754\end{array} \right]A=[34​21​​528.754​]

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - +=80 -=48

Find the inverse, if it exists, for the matrix. - [6−34−36−2−3−212−51−50−680]\left[ \begin{array} { r r r r } 6 & - 3 & 4 & - 3 \\6 & - 2 & - 3 & - 2 \\12 & - 5 & 1 & - 5 \\0 & - 6 & 8 & 0\end{array} \right]​66120​−3−2−5−6​4−318​−3−2−50​​

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - 2x-y-5z=-14 -2x+4y+4z=16 -8x-4y+z=-36

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. - 3x+y=10 9x+4y=25

Solve the equation for x. - ∣x12x∣=−1\left| \begin{array} { l l } x & 1 \\2 & x\end{array} \right| = - 1​x2​1x​​=−1

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - y=|x| 4x-y=-20

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - 1.2x+y=-8 -4.5x-y=10

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. -A is 2×22 \times 22×2 ; B is 2×22 \times 22×2 .

Which method should be used to solve the system? Explain your answer, including a description of the first step. - (x−3)2+(y−1)2≤9( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } \leq 9(x−3)2+(y−1)2≤9

Find the matrix product when possible. - [3−160][0−126]\left[ \begin{array} { r r } 3 & - 1 \\6 & 0\end{array} \right] \left[ \begin{array} { r r } 0 & - 1 \\2 & 6\end{array} \right][36​−10​][02​−16​]

Provide an appropriate response. -Fill in the blank to complete the statement. Each number in a matrix is called of the matrix.

Solve the system by substitution. - x+8y=35 2x+8y=30

Solve the equation for x. - ∣x005x1321∣=−1\left| \begin{array} { l l l } x & 0 & 0 \\5 & x & 1 \\3 & 2 & 1\end{array} \right| = - 1​x53​0x2​011​​=−1

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Filters

Provide an appropriate response. -Let $A = \left[ \begin{array} { r r } - 4 & - 4 \\ - 6 & 3 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 1 & 4 \\ 5 & - 3 \end{array} \right]$ Does the matrix $A + B$ have an inverse?

Solve the equation for x. - $\left| \begin{array} { l l } x & 3 \\2 & 1\end{array} \right| = 6$

Use a graphing calcula tor to find the inverse of the matrix. Give five decimal places, if necessary. - $A = \left[ \begin{array} { c c } \frac { 4 } { 3 } & 52 \\\sqrt { 21 } & 8.754\end{array} \right]$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r r } 6 & - 3 & 4 & - 3 \\6 & - 2 & - 3 & - 2 \\12 & - 5 & 1 & - 5 \\0 & - 6 & 8 & 0\end{array} \right]$

Solve the equation for x. - $\left| \begin{array} { l l } x & 1 \\2 & x\end{array} \right| = - 1$

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. -A is $2 \times 2$ ; B is $2 \times 2$ .

Find the matrix product when possible. - $\left[ \begin{array} { r r } 3 & - 1 \\6 & 0\end{array} \right] \left[ \begin{array} { r r } 0 & - 1 \\2 & 6\end{array} \right]$

Solve the equation for x. - $\left| \begin{array} { l l l } x & 0 & 0 \\5 & x & 1 \\3 & 2 & 1\end{array} \right| = - 1$