If A- 1 2 -3- 5 0 2- 1 -1 1 -B- 3 -1 2- 4 2 5- 2 0 3 -C- 4 1 2- 0 3 2- 1 -2 3 - Then Compute A-B and B-C- Also- verify that A-B-C-A-B-C

A+B=[ 1+3 amp; 2 1 amp; 3+2; 5+4 amp; 0+2 amp; nbsp;2+5; 1+2 amp; 1+0 amp; 1+3 ] =[ 4 amp;1 amp; 1; 9 amp ...

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Byju's Answer

Standard XII

Mathematics

Multiplication of Matrices

If A=[ 1 2 ...

Question

If $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & - 3 5 & 0 & 2 1 & - 1 & 1 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 3 & - 1 & 2 4 & 2 & 5 2 & 0 & 3 \end{matrix} ⎤ ⎥ ⎦, C = ⎡ ⎢ ⎣ \begin{matrix} 4 & 1 & 2 0 & 3 & 2 1 & - 2 & 3 \end{matrix} ⎤ ⎥ ⎦$ , Then Compute $(A + B)$ and $(B - C)$ . Also, verify that $A + (B - C) = (A + B) - C$

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Solution

$A + B = ⎡ ⎢ ⎣ \begin{matrix} 1 + 3 & 2 - 1 & - 3 + 2 5 + 4 & 0 + 2 & 2 + 5 1 + 2 & - 1 + 0 & 1 + 3 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 4 & 1 & - 1 9 & 2 & 7 3 & - 1 & 4 \end{matrix} ⎤ ⎥ ⎦ B - C = ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 2 & 0 4 & - 1 & 3 1 & 2 & 0 \end{matrix} ⎤ ⎥ ⎦ A + (B - C) = ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 & 2 - 2 & - 3 + 0 5 + 4 & 0 - 1 & 2 + 3 1 + 1 & - 1 + 2 & 1 + 0 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0 & 0 & - 3 9 & - 1 & 5 2 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦ (A + B) - C = ⎡ ⎢ ⎣ \begin{matrix} 4 - 4 & 1 - 1 & - 1 - 2 9 - 0 & 2 - 3 & 7 - 2 3 - 1 & - 1 + 2 & 4 - 3 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0 & 0 & - 3 9 & - 1 & 5 2 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦$

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Similar questions

Q. A =

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & - 3 5 & 0 & 2 1 & - 1 & 1 \end{matrix} ⎤ ⎥ ⎦

and B =

⎡ ⎢ ⎣ \begin{matrix} 3 & - 1 & 2 4 & 2 & 5 2 & 0 & 3 \end{matrix} ⎤ ⎥ ⎦

Find the matrix C satisfying the relation A + 2C = B

Q. If

A = ⎡ ⎢ ⎣ \begin{matrix} 151 \end{matrix} \begin{matrix} 20 - 1 \end{matrix} \begin{matrix} - 3 21 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 342 \end{matrix} \begin{matrix} - 1 20 \end{matrix} \begin{matrix} 253 \end{matrix} ⎤ ⎥ ⎦

and

C = ⎡ ⎢ ⎣ \begin{matrix} 401 \end{matrix} \begin{matrix} 13 - 2 \end{matrix} \begin{matrix} 223 \end{matrix} ⎤ ⎥ ⎦

, then compute

(A + B)

and

(B - C)

Also, verify that

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

Q. Given

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & - 3 5 & 0 & 2 1 & - 1 & 1 \end{matrix} ⎤ ⎥ ⎦

and

B = ⎡ ⎢ ⎣ \begin{matrix} 3 & - 1 & 2 4 & 2 & 5 2 & 0 & 3 \end{matrix} ⎤ ⎥ ⎦

.
Find the matrix

C

such that

A + 2 C = B

C = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 1 & \frac{- 3}{2} & a \frac{- 1}{2} & 1 & b \frac{1}{2} & \frac{1}{2} & 1 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

Find the value of a+b?

$A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & - 3 5 & 0 & 2 1 & - 1 & 1 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 3 & - 1 & 2 4 & 2 & 5 2 & 0 & 3 \end{matrix} ⎤ ⎥ ⎦, C = ⎡ ⎢ ⎣ \begin{matrix} 4 & 1 & 2 0 & 3 & 2 1 & - 2 & 3 \end{matrix} ⎤ ⎥ ⎦$ compute (A+B) and (B-C). Also verify that A+(B-C)=(A+B)-C.

Q. If

A = (\begin{matrix} 4 & 1 & 2 1 & - 2 & 3 0 & 3 & 2 \end{matrix}), B = (\begin{matrix} 2 & 0 & 4 6 & 2 & 8 2 & 4 & 6 \end{matrix})

and

C = (\begin{matrix} 1 & 2 & - 3 5 & 0 & 2 1 & - 1 & 1 \end{matrix})

, then
verify that

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

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If A=⎡⎢⎣12−35021−11⎤⎥⎦,B=⎡⎢⎣3−12425203⎤⎥⎦,C=⎡⎢⎣4120321−23⎤⎥⎦, Then Compute (A+B) and (B−C). Also, verify that A+(B−C)=(A+B)−C