If A- 1 2- 2 1 -B - - 2 0- 1 3 - and C- 1 1- 2 3 - calculate AC- BC and A-BC- Also verify that A-BC-AC-BC-

Given A=[ 1 amp; 2; 2 amp; 1 ] , B=[ 2 amp; 0; 1 amp; 3 ] and C=[ 1 amp; 1; 2 amp; 3 ] AC =[ 1 amp; 2; ...

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Byju's Answer

Standard XII

Mathematics

Multiplication of Matrices

If A=[ 1 2;...

Question

If $A = [\begin{matrix} 1 & 2 2 & 1 \end{matrix}] . B = [\begin{matrix} 2 & 0 1 & 3 \end{matrix}]$ and $C = [\begin{matrix} 1 & 1 2 & 3 \end{matrix}]$ calculate $A C, B C$ and $(A + B) C$ . Also verify that $(A + B) C = A C + B C .$

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Solution

Given $A = [\begin{matrix} 1 & 2 2 & 1 \end{matrix}]$ , $B = [\begin{matrix} 2 & 0 1 & 3 \end{matrix}]$ and $C = [\begin{matrix} 1 & 1 2 & 3 \end{matrix}]$

$A C = [\begin{matrix} 1 & 2 2 & 1 \end{matrix}] [\begin{matrix} 1 & 1 2 & 3 \end{matrix}] = [\begin{matrix} 5 & 7 4 & 5 \end{matrix}]$

$B C = [\begin{matrix} 2 & 0 1 & 3 \end{matrix}] [\begin{matrix} 1 & 1 2 & 3 \end{matrix}] = [\begin{matrix} 2 & 2 7 & 10 \end{matrix}]$

$(A + B) C = ([\begin{matrix} 1 & 2 2 & 1 \end{matrix}] + [\begin{matrix} 2 & 0 1 & 3 \end{matrix}]) [\begin{matrix} 1 & 1 2 & 3 \end{matrix}] = [\begin{matrix} 3 & 2 3 & 4 \end{matrix}] [\begin{matrix} 1 & 1 2 & 3 \end{matrix}] = [\begin{matrix} 7 & 9 11 & 15 \end{matrix}]$
Also, $A C + B C = [\begin{matrix} 5 & 7 4 & 5 \end{matrix}] + [\begin{matrix} 2 & 2 7 & 10 \end{matrix}] = [\begin{matrix} 7 & 9 11 & 15 \end{matrix}]$
Hence, $(A + B) C = A C + B C$

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Similar questions

Q. If

A = ⎡ ⎢ ⎣ \begin{matrix} 0 & 6 & 7 - 6 & 0 & 8 7 & - 8 & 0 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 0 & 1 & 1 1 & 0 & 2 1 & 2 & 0 \end{matrix} ⎤ ⎥ ⎦, C = ⎡ ⎢ ⎣ \begin{matrix} 2 - 2 3 \end{matrix} ⎤ ⎥ ⎦

, calculate

A C, B C

and

(A + B) C

.
Also, verify that

(A + B) C = A C + B C

Using elementary row operations (transformations), find the inverse of $⎛ ⎜ ⎝ \begin{matrix} 0 & 1 & 2 1 & 2 & 3 3 & 1 & 0 \end{matrix} ⎞ ⎟ ⎠$ OR If A = $⎡ ⎢ ⎣ \begin{matrix} 0 & 6 & 7 - 6 & 0 & 8 7 & - 8 & 0 \end{matrix} ⎤ ⎥ ⎦$ , B = $⎡ ⎢ ⎣ \begin{matrix} 0 & 1 & 1 1 & 0 & 2 1 & 2 & 0 \end{matrix} ⎤ ⎥ ⎦$ , C= $⎡ ⎢ ⎣ \begin{matrix} 2 - 2 3 \end{matrix} ⎤ ⎥ ⎦$ , then calculate AC, BC and (A+B) C.