If A = [2-3532-411-2], find A–1. Use A–1 to solve the following system of equations 2x − 3y + 5z = 11, 3x + 2y – 4z = –5, x + y – 2z = –3 - Mathematics

Question

If A = $[\begin{matrix} 2 & - 3 & 5 \\ 3 & 2 & - 4 \\ 1 & 1 & - 2 \end{matrix}]$ , find A^–1. Use A^–1 to solve the following system of equations 2x − 3y + 5z = 11, 3x + 2y – 4z = –5, x + y – 2z = –3

Sum

Solution

A = $[\begin{matrix} 2 & - 3 & 5 \\ 3 & 2 & - 4 \\ 1 & 1 & - 2 \end{matrix}]$

|A| = 2(0) + 3(–2) + 5(1) = –1

A^–1 = $\frac{a d j A}{| A |}$

adj A = $[\begin{matrix} 0 & - 1 & 2 \\ 2 & - 9 & 23 \\ 1 & - 5 & 13 \end{matrix}]$ , A^–1 = $\frac{1}{(- 1)} [\begin{matrix} 0 & - 1 & 2 \\ 2 & - 9 & 23 \\ 1 & - 5 & 13 \end{matrix}]$

X = A^–1B

⇒ $[\begin{matrix} x \\ y \\ z \end{matrix}]$

= $\frac{1}{(- 1)} [\begin{matrix} 0 & - 1 & 2 \\ 2 & - 9 & 23 \\ 1 & - 5 & 13 \end{matrix}] [\begin{matrix} 11 \\ - 5 \\ - 3 \end{matrix}]$

= $\frac{1}{(- 1)} [\begin{matrix} 0 + 5 - 6 \\ 22 + 45 - 69 \\ 11 + 25 - 39 \end{matrix}]$

⇒ $[\begin{matrix} x \\ y \\ z \end{matrix}] = \frac{1}{(- 1)} [\begin{matrix} - 1 \\ - 2 \\ - 3 \end{matrix}]$

⇒ x = 1, y = 2, z = 3.

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If A = [2-3532-411-2], find A–1. Use A–1 to solve the following system of equations 2x − 3y + 5z = 11, 3x + 2y – 4z = –5, x + y – 2z = –3 - Mathematics

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If A = [2-3532-411-2], find A–1. Use A–1 to solve the following system of equations 2x − 3y + 5z = 11, 3x + 2y – 4z = –5, x + y – 2z = –3 - Mathematics

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