91Ó°ÊÓ

Find the value of each expression. $$ \frac{1}{2}(34) $$

For matrix \(A=\left[\begin{array}{ll}{1} & {2} \\ {3} & {4}\end{array}\right],\) the transpose of \(A\) is \(A^{T}=\left[\begin{array}{ll}{1} & {3} \\ {2} & {4}\end{array}\right]\) Write a matrix \(B\) that is equal to its transpose \(B^{T}\) .

OPEN ENDED Create a square matrix that does not have an inverse. Explain how you know it has no inverse.

Find each product, if possible. \(\left[\begin{array}{rr}{0} & {9} \\ {5} & {7}\end{array}\right] \cdot\left[\begin{array}{rr}{2} & {-6} \\ {8} & {1}\end{array}\right]\)

Find each product, if possible. $$ \left[\begin{array}{rr}{2} & {4} \\ {-2} & {3}\end{array}\right] \cdot\left[\begin{array}{rr}{3} & {9} \\ {-1} & {2}\end{array}\right] $$

CHALLENGE For which values of \(a, b, c,\) and \(d\) will \(A=\left[\begin{array}{ll}{a} & {b} \\ {c} & {d}\end{array}\right]=A^{-1} ?\)

Find each product, if possible. \(\left[\begin{array}{rr}{5} & {-4} \\ {8} & {3}\end{array}\right] \cdot\left[\begin{array}{l}{5} \\ {1}\end{array}\right]\)

Find the value of each expression. $$ -5(3-18) $$

Perform the indicated matrix operations. If the matrix does not exist, write impossible. 3\(\left[\begin{array}{rr}{4} & {-2} \\ {-1} & {7}\end{array}\right]\)

ACT/SAT Triangle \(A B C\) has vertices with coordinates \(A(-4,2), B(-4,-3)\) and \(C(3,-2) .\) After a dilation, triangle \(A^{\prime} B^{\prime} C^{\prime}\) has coordinates \(A^{\prime}(-12,6)\) \(B^{\prime}(-12,-9),\) and \(C^{\prime}(9,-6) .\) How many times as great is the perimeter of \(\triangle A^{\prime} B^{\prime} C^{\prime}\) as that of \(\triangle A B C ?\) A 3 B 6 C 12 D \(\frac{1}{3}\)