Find x and y, if {4[2-13102]-[3-34211]}[2-11]=[xy] - Mathematics and Statistics

प्रश्न

Find x and y, if ${4 [\begin{matrix} 2 & - 1 & 3 \\ 1 & 0 & 2 \end{matrix}] - [\begin{matrix} 3 & - 3 & 4 \\ 2 & 1 & 1 \end{matrix}]} [\begin{matrix} 2 \\ - 1 \\ 1 \end{matrix}] = [\begin{matrix} x \\ y \end{matrix}]$

बेरीज

उत्तर

${4 [\begin{matrix} 2 & - 1 & 3 \\ 1 & 0 & 2 \end{matrix}] - [\begin{matrix} 3 & - 3 & 4 \\ 2 & 1 & 1 \end{matrix}]} [\begin{matrix} 2 \\ - 1 \\ 1 \end{matrix}] = [\begin{matrix} x \\ y \end{matrix}]$

∴ ${[\begin{matrix} 8 & - 4 & 12 \\ 4 & 0 & 8 \end{matrix}] - [\begin{matrix} 3 & - 3 & 4 \\ 2 & 1 & 1 \end{matrix}]} [\begin{matrix} 2 \\ - 1 \\ 1 \end{matrix}] = [\begin{matrix} x \\ y \end{matrix}]$

∴ $[\begin{matrix} 8 - 3 & - 4 + 3 & 12 - 4 \\ 4 - 2 & 0 - 1 & 8 - 1 \end{matrix}] [\begin{matrix} 2 \\ - 1 \\ 1 \end{matrix}] = [\begin{matrix} x \\ y \end{matrix}]$

∴ $[\begin{matrix} 5 & - 1 & 8 \\ 2 & - 1 & 7 \end{matrix}] [\begin{matrix} 2 \\ - 1 \\ 1 \end{matrix}] = [\begin{matrix} x \\ y \end{matrix}]$

∴ $[\begin{matrix} 10 + 1 + 8 \\ 4 + 1 + 7 \end{matrix}] = [\begin{matrix} x \\ y \end{matrix}]$

∴ $[\begin{matrix} 19 \\ 12 \end{matrix}] = [\begin{matrix} x \\ y \end{matrix}]$

∴ By equality of matrices, we get

x = 19 and y = 12

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Matrices - Properties of Matrix Multiplication

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Q 21 Q 20 Q 22

पाठ 4: Determinants and Matrices - Exercise 4.6 [पृष्ठ ९५]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board

पाठ 4 Determinants and Matrices
Exercise 4.6 | Q 21 | पृष्ठ ९५

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