Exam 6: Matrices and Determinants and Applications

Perform the indicated operations. -Find -5A - 4B. $A = \left[ \begin{array} { r r r } 3 & - 8 & - 4 \\ - 4 & 6 & 9 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 4 & 5 & - 1 \\ - 4 & 5 & - 6 \end{array} \right]$

Solve the system, if possible, by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. - -12(x+y)=-4x-28 -2x=3y-7

Perform the elementary row operation on the given matrix. - $- 5 R _ { 1 } + R _ { 3 } \rightarrow R _ { 3 }$ $\left[ \begin{array} { r r r | r } 1 & 16 & 5 & 3 \\ 7 & 18 & 5 & 8 \\ 5 & 12 & 9 & 13 \end{array} \right]$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given an n × n matrix A, if there exists a matrix $A ^ { - 1 }$ such that $A \cdot A ^ { - 1 } = I _ { n } \text { and } A ^ { - 1 } \cdot A = I _ { n } \text {, then } A ^ { - 1 } \text { is }$ called the ________of A.

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - 5x+9z=-16+6y 8x=7y+7z-141 8z=-2y-2x+42

Determine the solution set for the system represented by the augmented matrix. - $\left[ \begin{array} { r r r | r } 1 & 0 & - 7 & 4 \\ 0 & 1 & 6 & 1 \\ 0 & 0 & 0 & 1 \end{array} \right]$

Evaluate the determinant of the given matrix and state whether the matrix is invertible. - $A = \left[ \begin{array} { r r r r } 0.9 & 1.7 & 8 & 12.7 \\- 3.5 & 0.4 & - 1.4 & 5 \\6 & 8.8 & - 4.4 & 2 \\- 2 & 3.5 & 11.4 & - 8.2\end{array} \right]$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If a system of linear equations has no solution, then the system is said to be________ .

Give the order of the matrix. Classify the matrix as a square matrix, row matrix, column matrix, or none of these. - $\left[ \begin{array} { c c c c } 1 & 5 & 8 & 7 \\- 2 & 2 & \frac { 2 } { 5 } & \pi \\0 & 1 & 0.6 & 11\end{array} \right]$

A rectangular array of elements is called a________ .

Solve the system, if possible, by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. - -6x-3y=2 -12x+15y=-6

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If A is a $5 \times 3$ 3 matrix and B is a $3 \times 7$ trix, then the product AB will be a matrix of order________. The product BA (is/is not) defined.

Evaluate the determinant of the given matrix and state whether the matrix is invertible. - $A = \left[ \begin{array} { r r r r } 1 & 2 & 0 & 4 \\0 & 3 & - 1 & 3 \\2 & 1 & 0 & 4 \\- 4 & 0 & 4 & 0\end{array} \right]$

Solve the problem. -A street vendor at a parade sells fresh lemonade, soda, bottled water, and iced-tea, and the unit price for each item is given in matrix P. The number of units sold of each item is given in matrix N.Compute NP and interpret the result. $\quad$ $\text { Lemonade }$$\quad$ $\text { Soda }$ $\quad$ $\text { Water }$ $\quad$$\text { Tea }$ N= 120 280 370 70 $P = \left[ \begin{array} { l | l } \$ 3.00 & \text { Lemonade } \\\$ 2.00 & \text { Soda } \\\$ 1.00 & \text { Water } \\\$ 1.50\end{array} \right] \text { Tea }$

Find AB, if possible. - $A = \left[ \begin{array} { l l l } 4 & 4 & 1 \\ 7 & 5 & 8 \end{array} \right]$ and $B = \left[ \begin{array} { c c } - 6 & 7 \\ 3 & 8 \\ 1 & 7 \end{array} \right]$

Classify the matrix as a square matrix, row matrix, column matrix, or none of these. - $\left[ \begin{array} { r r } 1 & 5 \\5 & - 3\end{array} \right]$

Find AB, if possible. - $A = \left[ \begin{array} { c c } 2 & - 1 \\ 6 & 5 \end{array} \right]$ and $B = \left[ \begin{array} { l l } 6 & 2 \\ 1 & 6 \end{array} \right]$

Solve the problem. - The matrix $\mathrm { A } = \left[ \begin{array} { r r r } - 1 & 1 & 4 \\ 1 & 4 & 3 \end{array} \right]$ represents the coordinates of the triangle. Find the product $\left[ \begin{array} { r r } 1 & 0 \\ 0 & - 1 \end{array} \right] \cdot \mathrm { A }$ and explain the effect on the graph of the triangle.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -True or false: If a row matrix A and a column matrix B have the same number of elements, then the product AB is well defined.

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - 5x-7y =-3 -6x+5y =7