If [14−23]+2M=3[320−3],\begin{bmatrix}[r] 1 & 4 \ -2 & 3 \end{bmatrix} + 2\text{M} = 3\begin{bmatrix}[r] 3 & 2 \ 0 & -3 \end{bmatrix}, \\[1em][1−243]+2M=3[302−3], find the matrix M.
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Given,
⇒[14−23]+2M=3[320−3]⇒[14−23]+2M=[960−9]⇒2M=[960−9]−[14−23]⇒2M=[9−16−40−(−2)−9−3]⇒M=12[822−12]⇒M=[411−6]\Rightarrow \begin{bmatrix}[r] 1 & 4 \ -2 & 3 \end{bmatrix} + 2\text{M} = 3\begin{bmatrix}[r] 3 & 2 \ 0 & -3 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 1 & 4 \ -2 & 3 \end{bmatrix} + 2\text{M} = \begin{bmatrix}[r] 9 & 6 \ 0 & -9 \end{bmatrix} \\[1em] \Rightarrow 2\text{M} = \begin{bmatrix}[r] 9 & 6 \ 0 & -9 \end{bmatrix} - \begin{bmatrix}[r] 1 & 4 \ -2 & 3 \end{bmatrix} \\[1em] \Rightarrow 2\text{M} = \begin{bmatrix}[r] 9 - 1 & 6 - 4 \ 0 - (-2) & -9 - 3 \end{bmatrix} \\[1em] \Rightarrow \text{M} = \dfrac{1}{2}\begin{bmatrix}[r] 8 & 2 \ 2 & -12 \end{bmatrix} \\[1em] \Rightarrow \text{M} = \begin{bmatrix}[r] 4 & 1 \ 1 & -6 \end{bmatrix} \\[1em]⇒[1−243]+2M=3[302−3]⇒[1−243]+2M=[906−9]⇒2M=[906−9]−[1−243]⇒2M=[9−10−(−2)6−4−9−3]⇒M=21[822−12]⇒M=[411−6]
Hence, matrix M = [411−6].\begin{bmatrix}[r] 4 & 1 \ 1 & -6 \end{bmatrix}.[411−6].
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If A = [0−112] and B=[12−11]\begin{bmatrix}[r] 0 & -1 \ 1 & 2 \end{bmatrix} \text{ and B} = \begin{bmatrix}[r] 1 & 2 \ -1 & 1 \end{bmatrix}[01−12] and B=[1−121], find the matrix X if
(i) 3A + X = B
(ii) X - 3B = 2A.
Solve the matrix equation [2150]−3X=[−7426]\begin{bmatrix} 2 & 1 \ 5 & 0 \end{bmatrix} - 3X = \begin{bmatrix}[r] -7 & 4 \ 2 & 6 \end{bmatrix}[2510]−3X=[−7246]
Given A=[2−620],B=[−3240] and C=[4002].A = \begin{bmatrix}[r] 2 & -6 \ 2 & 0 \end{bmatrix}, B = \begin{bmatrix}[r] -3 & 2 \ 4 & 0 \end{bmatrix} \text{ and } C = \begin{bmatrix}[r] 4 & 0 \ 0 & 2 \end{bmatrix}.A=[22−60],B=[−3420] and C=[4002].
Find the matrix X such that A + 2X = 2B + C.
Find X and Y if
X + Y=[7025] and X - Y=[3003].\text{X + Y} = \begin{bmatrix} 7 & 0 \ 2 & 5 \end{bmatrix} \text{ and X - Y} = \begin{bmatrix} 3 & 0 \ 0 & 3 \end{bmatrix}.X + Y=[7205] and X - Y=[3003].
