Evaluate - if possible- i- 3 2 - 2- 0 - ii - 1 -2 - -2 3- -1 4 - iii - 6 4- 3 -1 - -1- 3 - iv- 6 4- 3 -1 - -1 3 - IF not possible Give a reason-

(i)[ 3 amp;2 ][ 2; 0 ] =[ 6+0 ] = [ 6 ] (ii)[ 1 amp; 2 ][ 2 amp;3; 1 amp; 4 ] = gt;[ 2+2 3 8] = [0 5] (iii)[ 6 ...

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Byju's Answer

Standard X

Mathematics

Multiplication of Matrices

Evaluate ; if...

Question

Evaluate ; if possible:
$(i) [\begin{matrix} 3 & 2 \end{matrix}] [\begin{matrix} 20 \end{matrix}] (i i) [\begin{matrix} 1 & - 2 \end{matrix}] [\begin{matrix} - 2 & 3 - 1 & 4 \end{matrix}] (i i i) [\begin{matrix} 6 & 4 3 & - 1 \end{matrix}] [\begin{matrix} - 1 3 \end{matrix}] (i v) [\begin{matrix} 6 & 4 3 & - 1 \end{matrix}] [\begin{matrix} - 1 & 3 \end{matrix}]$
IF not possible Give a reason.

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Solution

$(i) [\begin{matrix} 3 & 2 \end{matrix}] [\begin{matrix} 20 \end{matrix}] = [\begin{matrix} 6 + 0 \end{matrix}] = [\begin{matrix} 6 \end{matrix}]$

(ii) $[\begin{matrix} 1 & - 2 \end{matrix}] [\begin{matrix} - 2 & 3 - 1 & 4 \end{matrix}]$
=>[-2+2 3-8] = [0 -5]

$(i i i) [\begin{matrix} 6 & 4 3 & - 1 \end{matrix}] [\begin{matrix} - 1 & 3 \end{matrix}] = [\begin{matrix} - 6 + 12 - 3 - 3 \end{matrix}] = [\begin{matrix} 6 - 6 \end{matrix}]$

iv) the number of columns in the first matrix is not equal to the number of rows in second matrix. Thus the product is not possible.

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$(i i) ⎡ ⎢ ⎣ \begin{matrix} 123 \end{matrix} ⎤ ⎥ ⎦ [234]$

$(i i i) [\begin{matrix} 1 & - 2 2 & 3 \end{matrix}] [\begin{matrix} 1 & 2 & 3 2 & 3 & 1 \end{matrix}]$

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$(v i) [\begin{matrix} 3 & - 1 & 3 - 1 & 0 & 2 \end{matrix}] ⎡ ⎢ ⎣ \begin{matrix} 2 & - 3 1 & 0 3 & 1 \end{matrix} ⎤ ⎥ ⎦$

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(ii)(A-B)'=A'-B'

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Evaluate ; if possible: (i)[32][20](ii)[1−2][−23−14](iii)[643−1][−13](iv)[643−1][−13] IF not possible Give a reason.

(i)[32][20]=[6+0]=[6] (ii)[1−2][−23−14] =>[-2+2 3-8] = [0 -5] (iii)[643−1][−13]=[−6+12−3−3]=[6−6] iv) the number of columns in the first matrix is not equal to the number of rows in second matrix. Thus the product is not possible.