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]
47 Likes
Given,
⇒[2150]−3X=[-7426]⇒3X=[2150]-[-7426]⇒3X=[2−(−7)1−45−20−6]⇒3X=[9−33−6]⇒X=13[9−33−6]⇒X=[3−11−2]\Rightarrow \begin{bmatrix} 2 & 1 \ 5 & 0 \end{bmatrix} - 3X = \begin{bmatrix}[r] -7 & 4 \ 2 & 6 \end{bmatrix} \\[1em] \Rightarrow 3X = \begin{bmatrix} 2 & 1 \ 5 & 0 \end{bmatrix} - \begin{bmatrix}[r] -7 & 4 \ 2 & 6 \end{bmatrix} \\[1em] \Rightarrow 3X = \begin{bmatrix}[r] 2 - (-7) & 1 - 4 \ 5 - 2 & 0 - 6 \end{bmatrix} \\[1em] \Rightarrow 3X = \begin{bmatrix}[r] 9 & -3 \ 3 & -6 \end{bmatrix} \\[1em] \Rightarrow X = \dfrac{1}{3}\begin{bmatrix}[r] 9 & -3 \ 3 & -6 \end{bmatrix} \\[1em] \Rightarrow X = \begin{bmatrix}[r] 3 & -1 \ 1 & -2 \end{bmatrix}⇒[2510]−3X=[-7246]⇒3X=[2510]-[-7246]⇒3X=[2−(−7)5−21−40−6]⇒3X=[93−3−6]⇒X=31[93−3−6]⇒X=[31−1−2]
Hence, matrix X = [3−11−2].\begin{bmatrix}[r] 3 & -1 \ 1 & -2 \end{bmatrix} .[31−1−2].
Answered By
18 Likes
If A =[12−23], B =[−2−112] and C=[032−1]\text{If A } = \begin{bmatrix}[r] 1 & 2 \ -2 & 3 \end{bmatrix}, \text{ B } = \begin{bmatrix}[r] -2 & -1 \ 1 & 2 \end{bmatrix} \text{ and C} = \begin{bmatrix}[r] 0 & 3 \ 2 & -1 \end{bmatrix}If A =[1−223], B =[−21−12] and C=[023−1], find A + 2B - 3C.
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.
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.
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.
