CPM Homework Help : PC Problem 12-19

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12-19.

Solve the following systems of equations.

Hint:

To solve each system, use matrices and calculate $A^{−1}B$ .

$\left. \begin{array} [t] { r } { x - 2 y = 7 } \\ { 5 x + 3 y = 9 } \end{array} \right.$
Step (a):
$A = \left[ \begin{array} { c c } { 1 }& {-2}\\ { 5 } & {3}\end{array} \right]$
$B = \left[ \begin{array} { c } { 7 } \\ { 9 } \end{array} \right]$
Solution (a):
$\left. \begin{array} { r } { \left[ \begin{array} { c } { x } \\ { y } \end{array} \right] = A ^ { - 1 } B } \\ { \left[ \begin{array} { c } { x } \\ { y } \end{array} \right] = \left[ \begin{array} { c } { 3 } \\ { - 2 } \end{array} \right] } \end{array} \right.$

$\left. \begin{array}[t] {l}{ x - y + 3 z = 2 }\\{ 4 x - 6 z = 19 }\\{ 4 y + 2 z = 1 }\end{array} \right.$
Step (b):
$A = \left[ \begin{array} { c c c } { 1 } & { - 1 } & { 3 } \\ { 4 } & { 0 } & { - 6 } \\ { 0 } & { 4 } & { 2 } \end{array} \right]$

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