Exam 6: Matrices and Determinants and Applications

Choose the one alternative that best completes the statement or answers the question. Evaluate the determinant of the given matrix. - $A = \left[ \begin{array} { r r } - 1 & 6 \\- 7 & - 9\end{array} \right]$

Solve the system, if possible, by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. - +5-3-5=-6 -3+=4 +5=-2 2-4=-8 Solve for $x _ { 3 } .$

Find A + B. - $A = \left[ \begin{array} { r r } - 6 & - 2 \\9 & 4 \\0 & 2\end{array} \right] , B = \left[ \begin{array} { r r } - 2 & 7 \\- 8 & - 1 \\8 & 4\end{array} \right]$

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - -3x-3y-3z=30 -9x-9y-9z=90 -1.5x-1.5y-1.5z=15

Find the indicated matrix. -Find $- 4 A - 5 ( A - B )$ $A = \left[ \begin{array} { r r r } 4 & 8 & 0 \\9 & 8 & - 4\end{array} \right] \text { and } B = \left[ \begin{array} { r r r } 8 & 2 & - 1 \\- 6 & 5 & 8\end{array} \right]$

________ row operations performed on an augmented matrix results in a new augmented matrix that represents an equivalent system of equations.

The solution set to a system of dependent equations is given. Write the specific solution corresponding to the given value of z. - $\{ ( 4 z - 7 , z - 4 , z ) \mid z$ is any real number $\}$ $z = - 5$

For what values of x, y, and z will A = B? - $A = \left[ \begin{array} { r r } - 2 & x \\z & 9\end{array} \right] \quad B = \left[ \begin{array} { l l } y & 3 \\8 & 9\end{array} \right]$

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - 8x+10y=-17 4x+5y=-9

Choose the one alternative that best completes the statement or answers the question. Write the augmented matrix for the given system. - 4(x-3y)=9y+6 8x=9y+6

Write a system of linear equations represented by the augmented matrix. - $\left[ \begin{array} { r r | r } 5 & 8 & 6 \\0 & - 5 & 11\end{array} \right]$

Find AB and BA. - $A = \left[ \begin{array} { r r } 2 & - 2 \\ - 3 & 9 \end{array} \right]$ and $B = \left[ \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right]$

Find AB, if possible. - $A = \left[ \begin{array} { r r r } 4 & 3 & 7 \\ - 3 & 8 & 0 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 6 & 7 & - 2 \\ 7 & 1 & - 6 \end{array} \right]$

Choose the one alternative that best completes the statement or answers the question. Evaluate the determinant of the given matrix. - $A = \left[ \begin{array} { c c } e ^ { x } & e ^ { 9 x } \\6 & - e ^ { 8 x }\end{array} \right]$

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - -2x-y+3z=13 x-3y-3z=-4

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Let $A = \left[ \begin{array} { l l } a & b \\c & d\end{array} \right]$ be an invertible matrix. Then a formula for the inverse A-1 is given by .

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - -3x-7y+7z=71 -2x+7y-3z=-22 -3x-9y+9z=87

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -What are the requirements for two matrices to be equal?

Explain the meaning of the notation $4 \mathrm { R } _ { 2 } + \mathrm { R } _ { 3 } \rightarrow \mathrm { R } _ { 3 }$

Use the formula $\text { Area } = \pm \frac { 1 } { 2 } \left| \begin{array} { l l l } x _ { 1 } & y _ { 1 } & 1 \\x _ { 2 } & y _ { 2 } & 1 \\x _ { 3 } & y _ { 3 } & 1\end{array} \right|$ to find the area of the triangle with the given vertices. Choose the + or - sign so that the value of the area is positive. - $( 5,4 ) , ( - 5,1 ) , ( - 2 , - 2 )$