If A- 1 5 1 2 0 -1 -3 2 1 - -B- 3 4 2 -1 2 0 2 5 3 - and C- 4 0 1 1 3 -2 2 2 3 - then compute A-B and B-C- Also- verify that A- B-C - A-B -C

A+B=[ 1 5 1 2 0 1 3 2 1 ] +[ 3 4 2 1 2 0 2 5 3 ] #160; =[ 1+3 ...

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Byju's Answer

Standard XII

Mathematics

Equality of Matrices

If A=[ 1 ...

Question

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

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Solution

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

$= ⎡ ⎢ ⎣ \begin{matrix} 1 + 3 5 + 4 1 + 2 \end{matrix} \begin{matrix} 2 - 1 0 + 2 - 1 + 0 \end{matrix} \begin{matrix} - 3 + 2 2 + 5 1 + 3 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 493 \end{matrix} \begin{matrix} 12 - 1 \end{matrix} \begin{matrix} - 1 74 \end{matrix} ⎤ ⎥ ⎦$

$B - C = ⎡ ⎢ ⎣ \begin{matrix} 342 \end{matrix} \begin{matrix} - 1 20 \end{matrix} \begin{matrix} 253 \end{matrix} ⎤ ⎥ ⎦ - ⎡ ⎢ ⎣ \begin{matrix} 401 \end{matrix} \begin{matrix} 13 - 2 \end{matrix} \begin{matrix} 223 \end{matrix} ⎤ ⎥ ⎦$

$= ⎡ ⎢ ⎣ \begin{matrix} 3 - 4 4 - 0 2 - 1 \end{matrix} \begin{matrix} - 1 - 1 2 - 3 0 - (- 2) \end{matrix} \begin{matrix} 2 - 2 5 - 2 3 - 3 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 1 41 \end{matrix} \begin{matrix} - 2 - 1 2 \end{matrix} \begin{matrix} 030 \end{matrix} ⎤ ⎥ ⎦$

$A + (B - C) = ⎡ ⎢ ⎣ \begin{matrix} 151 \end{matrix} \begin{matrix} 20 - 1 \end{matrix} \begin{matrix} - 3 21 \end{matrix} ⎤ ⎥ ⎦ + ⎡ ⎢ ⎣ \begin{matrix} - 1 41 \end{matrix} \begin{matrix} - 2 - 1 2 \end{matrix} \begin{matrix} 030 \end{matrix} ⎤ ⎥ ⎦$

$= ⎡ ⎢ ⎣ \begin{matrix} 1 + (- 1) 5 + 4 1 + 1 \end{matrix} \begin{matrix} 2 + (- 2) 0 + (- 1) - 1 + 2 \end{matrix} \begin{matrix} - 3 + 0 2 + 3 1 + 0 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 092 \end{matrix} \begin{matrix} 0 - 1 1 \end{matrix} \begin{matrix} - 3 51 \end{matrix} ⎤ ⎥ ⎦$

$(A + B) - C = ⎡ ⎢ ⎣ \begin{matrix} 493 \end{matrix} \begin{matrix} 12 - 1 \end{matrix} \begin{matrix} - 1 74 \end{matrix} ⎤ ⎥ ⎦ - ⎡ ⎢ ⎣ \begin{matrix} 401 \end{matrix} \begin{matrix} 13 - 2 \end{matrix} \begin{matrix} 223 \end{matrix} ⎤ ⎥ ⎦$

$= ⎡ ⎢ ⎣ \begin{matrix} 4 - 4 9 - 0 3 - 1 \end{matrix} \begin{matrix} 1 - 1 2 - 3 - 1 - (- 2) \end{matrix} \begin{matrix} - 1 - 2 7 - 2 4 - 3 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 092 \end{matrix} \begin{matrix} 0 - 1 1 \end{matrix} \begin{matrix} - 3 51 \end{matrix} ⎤ ⎥ ⎦$

Hence, we have verified that $A + (B - C) = (A + B) - C$ .

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Similar questions

Q. 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

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