First slide

Operations of matrix

Question

Solve for $x$ and $y$ , $x [\begin{array}{l} 2 \\ 1 \end{array}] + y [\begin{array}{l} 3 \\ 5 \end{array}] + [\begin{array}{l} - 8 \\ - 11 \end{array}] = 0$

Very Easy

A

1, 2
B

2,3
C

4,5
D

2,1

Solution

$x [\begin{array}{l} 2 \\ 1 \end{array}] + y [\begin{array}{l} 3 \\ 5 \end{array}] + [\begin{array}{l} - 8 \\ - 11 \end{array}] = 0$
$[\begin{array}{l} 2 x \\ x \end{array}] + [\begin{array}{l} 3 y \\ 5 y \end{array}] + [\begin{array}{l} - 8 \\ - 11 \end{array}] = 0$
$[\begin{array}{l} 2 x 3y -8 \\ x 5y -11 \end{array}] = [\begin{array}{l} 0 \\ 0 \end{array}]$
$\Rightarrow 2 x + 3 y-8 =0$ -----------(1)
$a n d x + 5 y-11 = 0$
$\Rightarrow 2 x + 10 y = 22$ -----------(2)
On subtracting eq. (1) from eq. (2), we get
$\begin{array}{l} - 7 y = - 14 \Rightarrow y = 2 \\ 2 x + 3 x 2 - 8 = 0 \\ 2 x = 2 \Rightarrow x = 1 \\ x = 1 and y = 2 \end{array}$

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