If [ 1 2 - 2 - b ] + [ a 4 3 2 ] = [ 5 6 1 0 ] , then a 2 + b 2 is equal to:

Question

If $[\begin{matrix} 1 & 2 \\ - 2 & - b \end{matrix}] + [\begin{matrix} a & 4 \\ 3 & 2 \end{matrix}] = [\begin{matrix} 5 & 6 \\ 1 & 0 \end{matrix}],$ then $a^{2} + b^{2}$ is equal to:

Smart Achievers · Accepted Answer

(1)

Ans. 20

Explanation:

We have,

$[\begin{matrix} 1 & 2 \\ - 2 & - b \end{matrix}] + [\begin{matrix} a & 4 \\ 3 & 2 \end{matrix}] = [\begin{matrix} 5 & 6 \\ 1 & 0 \end{matrix}]$

$\Rightarrow$ $[\begin{matrix} a + 1 & 6 \\ 1 & 2 - b \end{matrix}] = [\begin{matrix} 5 & 6 \\ 1 & 0 \end{matrix}]$

$\Rightarrow$ $a + 1 = 5, 2 - b = 0$

$\Rightarrow$ $a = 4, b = 2$

$\Rightarrow$ $a^{2} + b^{2} = 4^{2} + 2^{2} = 20$

Solution

Q.
If $[\begin{matrix} 1 & 2 \\ - 2 & - b \end{matrix}] + [\begin{matrix} a & 4 \\ 3 & 2 \end{matrix}] = [\begin{matrix} 5 & 6 \\ 1 & 0 \end{matrix}],$ then $a^{2} + b^{2}$ is equal to:

1 20

2 22

3 12

4 10

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