Find Matrices X And Y, If 2x − Y = `[[6 -6 0],[-4 2 1]]`And X + 2y =`[[3 2 5],[-2 1 -7 ]]` - Mathematics

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Find matrices X and Y, if 2X − Y = $[\begin{matrix} 6 - 6 0 \\ - 4 2 1 \end{matrix}]$ and X + 2Y = $[\begin{matrix} 3 2 5 \\ - 2 1 - 7 \end{matrix}]$

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$G i v e n : (2 X - Y) = [\begin{matrix} 6 & - 6 & 0 \\ - 4 & 2 & 1 \end{matrix}] . . . (1)$
$(X + 2 Y) = [\begin{matrix} 3 & 2 & 5 \\ - 2 & 1 & - 7 \end{matrix}] . . . (2)$
Multiplying eq. (1) by eq. (2), we get
$2 (2 X - Y) = 2 [\begin{matrix} 6 & - 6 & 0 \\ - 4 & 2 & 1 \end{matrix}]$
$\Rightarrow 4 X - 2 Y = [\begin{matrix} 12 & - 12 & 0 \\ - 8 & 4 & 2 \end{matrix}] . . . (3)$
From eq. (3) and eq. (4) , we get
$(4 X - 2 Y) + (X + 2 Y) = [\begin{matrix} 12 & - 12 & 0 \\ - 8 & 4 & 2 \end{matrix}] + [\begin{matrix} 3 & 2 & 5 \\ - 2 & 1 & - 7 \end{matrix}]$
$\Rightarrow 5 X = [\begin{matrix} 12 + 3 & - 12 + 2 & 0 + 5 \\ - 8 - 2 & 4 + 1 & 2 - 7 \end{matrix}]$
$\Rightarrow 5 X = [\begin{matrix} 15 & - 10 & 5 \\ - 10 & 5 & - 5 \end{matrix}]$
$\Rightarrow X = \frac{1}{5} [\begin{matrix} 15 & - 10 & 5 \\ - 10 & 5 & - 5 \end{matrix}]$
$\Rightarrow X = [\begin{matrix} 3 & - 2 & 1 \\ - 2 & 1 & - 1 \end{matrix}]$
Putting the value of X in eq . ( 2 ), we get
$(X + 2 Y) = [\begin{matrix} 3 & 2 & 5 \\ - 2 & 1 & - 7 \end{matrix}]$
$\Rightarrow [\begin{matrix} 3 & - 2 & 1 \\ - 2 & 1 & - 1 \end{matrix}] + 2 Y = [\begin{matrix} 3 & 2 & 5 \\ - 2 & 1 & - 7 \end{matrix}]$
$\Rightarrow 2 Y = [\begin{matrix} 3 & 2 & 5 \\ - 2 & 1 & - 7 \end{matrix}] - [\begin{matrix} 3 & - 2 & 1 \\ - 2 & 1 & - 1 \end{matrix}]$
$\Rightarrow 2 Y = [\begin{matrix} 3 - 3 & 2 + 2 & 5 - 1 \\ - 2 + 2 & 1 - 1 & - 7 + 1 \end{matrix}]$
$\Rightarrow Y = [\begin{matrix} 0 & 2 & 2 \\ 0 & 0 & - 3 \end{matrix}]$

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Algebraic Operations on Matrices - Addition of Matrices

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पाठ 5: Algebra of Matrices - Exercise 5.2 [पृष्ठ १८]

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पाठ 5 Algebra of Matrices
Exercise 5.2 | Q 9 | पृष्ठ १८

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Algebraic Operations on Matrices - Addition of Matrices

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Find Matrices X And Y, If 2x − Y = [6-60-421]And X + 2y =[325-21-7] - Mathematics

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Find Matrices X And Y, If 2x − Y = $[\begin{matrix} 6 - 60 \\ - 421 \end{matrix}]$ And X + 2y = $[\begin{matrix} 325 \\ - 21 - 7 \end{matrix}]$ - Mathematics

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