Let A - begin bmatrix 2 - 1110 -2lend bmatrix - B - begin bmatrix 4 - 111-3 -2lend bmatrix and C - bmatrix -3 - 2 1-1 - 4lendbmatrix Find- A2-A C-5 BA- Wbeginbmatrix - 0 10 - 1lendbmatrix B- Vbeginbmatrix 23 - 3 117 - 6lendbmatrix C- beginbmatrix -23 - 3 117 - x-6 e n d b m a t r i x D- beginbmatrix -23 - 3 117 - 6lendbmatrix

The correct option is D [ 23 amp; 3; 17 amp; 6 ] A^2=[ 2 amp; 1; 0 amp; 2 ][ 2 amp; 1; 0 amp; 2 ] = [ 2 × 2 + 1 × 0 ...

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Byju's Answer

Standard X

Mathematics

Addition and Subtraction of a Matrix

Let A = begin...

Question

Let $A = [\begin{matrix} 2 & 1 0 & - 2 \end{matrix}], B = [\begin{matrix} 4 & 1 - 3 & - 2 \end{matrix}]$ and $C = [\begin{matrix} - 3 & 2 - 1 & 4 \end{matrix}]$ Find: $A^{2} + A C - 5 B$

$[\begin{matrix} 1 & 0 0 & 1 \end{matrix}]$

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$[\begin{matrix} 23 & 3 17 & 6 \end{matrix}]$

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$[\begin{matrix} - 23 & 3 17 & - 6 \end{matrix}]$

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$[\begin{matrix} - 23 & 3 17 & 6 \end{matrix}]$

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Solution

The correct option is D
$[\begin{matrix} - 23 & 3 17 & 6 \end{matrix}]$

$A^{2} = [\begin{matrix} 2 & 1 0 & - 2 \end{matrix}] [\begin{matrix} 2 & 1 0 & - 2 \end{matrix}] = [\begin{matrix} 2 \times 2 + 1 \times 0 & 2 \times 1 + 1 \times - 2 0 \times 2 + - 2 \times 0 & 0 \times 1 + (- 2) (- 2) \end{matrix}] = [\begin{matrix} 4 & 0 0 & 4 \end{matrix}]$

$A C = [\begin{matrix} 2 & 1 0 & - 2 \end{matrix}] [\begin{matrix} - 3 & 2 - 1 & 4 \end{matrix}]$

$= [\begin{matrix} - 3 \times 2 + 1 \times - 1 & 2 \times 2 + 1 \times 4 0 \times - 3 + (- 2) \times (- 1) & 0 \times 2 + (- 2 \times 4) \end{matrix}] = [\begin{matrix} - 7 & 8 2 & - 8 \end{matrix}]$

$5 B = [\begin{matrix} 20 & 5 - 15 & - 10 \end{matrix}]$

$A^{2} + A C - 5 B = [\begin{matrix} 4 & 0 0 & + 4 \end{matrix}] + [\begin{matrix} - 7 & 8 2 & - 8 \end{matrix}] - [\begin{matrix} 20 & 5 - 15 & - 10 \end{matrix}] = [\begin{matrix} - 23 & 3 17 & 6 \end{matrix}]$

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Let A=[210−2],B=[41−3−2] and C=[−32−14] Find: A2+AC−5B

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