CHAPTER 16 REVIEW EXERCISES

CONCEPT CHECK EXERCISES

Determine each of the following as being either true or false. If it is false, explain why.

$2 [\begin{array}{r} 3 & - 1 \\ 0 & - 2 \end{array}] = [\begin{array}{r} 6 & - 2 \\ 0 & 2 \end{array}]$
$[\begin{array}{r} 3 & - 1 \\ 0 & 2 \end{array}] [\begin{array}{r} 1 & 3 \\ - 2 & - 1 \end{array}] = [\begin{array}{r} 5 & 10 \\ - 4 & - 2 \end{array}]$
If $A = [\begin{array}{r} - 1 & 1 \\ 4 & - 3 \end{array}],$ then $A^{- 1} = [\begin{array}{r} - 3 & - 1 \\ - 4 & - 1 \end{array}]$
$| \begin{array}{r} 3 & 1 & - 1 \\ 2 & - 2 & 3 \\ 0 & 1 & 2 \end{array} | = 3 | \begin{array}{r} - 2 & 3 \\ 1 & 2 \end{array} | - 2 | \begin{array}{r} 1 & - 1 \\ 1 & 2 \end{array} |$
$[\begin{array}{r} 2 & - 1 \\ 5 & - 3 \end{array}] [\begin{array}{r} 3 \\ 7 \end{array}] = [\begin{array}{r} - 1 \\ - 6 \end{array}]$ is the matrix solution of $\begin{array}{l} 2 x - y = 3 \\ 5 x - 3 y = 7 \end{array} .$
After using two steps of the Gaussian elimination method for solving the system $\begin{array}{l} 2 x + 3 y = 4 \\ 3 x + 2 y = 1 \end{array},$ we would have $\begin{array}{c} x + \frac{3}{2} y = 1 \\ - \frac{5}{2} y = - 5 \end{array} .$

In Exercises 7–12, determine the values of the literal numbers.

$[\begin{array}{c} 4 a \\ a - b \end{array}] = [\begin{array}{c} 8 \\ 5 \end{array}]$
$[\begin{array}{c} x - y \\ 2 x + 2 z \\ 4 y + z \end{array}] = [\begin{array}{r} 1 \\ 3 \\ - 1 \end{array}]$
$[$

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