Find a matrix A such that 2 A -3 B -5 C - O- where B - begin bmatrix -2 - 2 - 0 cr3 - 1 - 42 - 0 -2 cr7 - 1 - 6endbmatrix -

Given, 2A 3B+5C=0 ⇒ 2A=3B 5C ⇒ 2A=3[ 2 nbsp; amp; 2 amp; 0 nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; n ...

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Byju's Answer

Standard XII

Mathematics

Elementary Transformations

Find a matrix...

Question

Find a matrix $A$ such that $2 A - 3 B + 5 C = O,$ where $B = [\begin{matrix} - 2 & 2 & 0 3 & 1 & 4 \end{matrix}] and C = [\begin{matrix} 2 & 0 & - 2 7 & 1 & 6 \end{matrix}] .$

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Solution

$Given, 2 A - 3 B + 5 C = 0 \Rightarrow 2 A = 3 B - 5 C \Rightarrow 2 A = 3 [\begin{matrix} - 2 & 2 & 0 3 & 1 & 4 \end{matrix}] - 5 [\begin{matrix} 2 & 0 & - 2 7 & 1 & 6 \end{matrix}] \Rightarrow 2 A = [\begin{matrix} - 6 & 6 & 0 9 & 3 & 12 \end{matrix}] - [\begin{matrix} 10 & 0 & - 10 35 & 5 & 30 \end{matrix}] \Rightarrow 2 A = [\begin{matrix} - 16 & 6 & 10 - 26 & - 2 & - 18 \end{matrix}] \Rightarrow A = [\begin{matrix} - 8 & 3 & 5 - 13 & - 1 & - 9 \end{matrix}]$

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Q. Find a matrix

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Find a matrix A such that 2A−3B+5C=O, where B=[−220314]and C=[20−2716].

Given, 2A−3B+5C=0⇒2A=3B−5C⇒2A=3[−220314]−5[20−2716]⇒2A=[−6609312]−[100−1035530]⇒2A=[−16610−26−2−18]⇒A=[−835−13−1−9]

Find a matrix $A$ such that $2 A - 3 B + 5 C = O,$ where $B = [\begin{matrix} - 2 & 2 & 0 3 & 1 & 4 \end{matrix}] and C = [\begin{matrix} 2 & 0 & - 2 7 & 1 & 6 \end{matrix}] .$