Using matrices, solve the following system of equations:
2x – 3y + 5 = 11
3x + 2y – 4z = -5
x + y – 2z= -3

Solution

2x - 3y + 5z = 11

3x + 2y - 4z = -5

x + y - 2z = -3

System of equations can be written as AX = B

$Where, A = [\begin{matrix} 2 & - 3 & 5 \\ 3 & 2 & - 4 \\ 1 & 1 & - 2 \end{matrix}] X = [\begin{matrix} x \\ y \\ z \end{matrix}] B = [\begin{matrix} 11 \\ - 5 \\ - 3 \end{matrix}] A = [\begin{matrix} 2 & - 3 & 5 \\ 3 & 2 & - 4 \\ 1 & 1 & - 2 \end{matrix}] |A| = 2 (- 4 + 4) + 3 (- 6 + 4) + 5 (3 - 2) |A| = - 6 + 5 = - 1 \neq 0 ∴ A^{- 1} exists and system of equation has unique solution A^{- 1} = \frac{1}{|A|} (adj A)$

$adj A = [\begin{matrix} 0 & - 1 & 2 \\ 2 & - 9 & 23 \\ 1 & - 5 & 13 \end{matrix}] A^{- 1} = \frac{1}{|A|} [\begin{matrix} 0 & - 1 & 2 \\ 2 & - 9 & 23 \\ 1 & - 5 & 13 \end{matrix}] = [\begin{matrix} 0 & 1 & - 2 \\ - 2 & 9 & - 23 \\ - 1 & 5 & - 13 \end{matrix}] X = A^{- 1} B = [\begin{matrix} 0 & 1 & - 2 \\ - 2 & 9 & - 23 \\ - 1 & 5 & - 13 \end{matrix}] [\begin{matrix} 11 \\ - 5 \\ - 3 \end{matrix}] X = [\begin{matrix} - 5 + 6 \\ - 22 - 45 + 69 \\ - 11 - 25 + 39 \end{matrix}] = [\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}]$

So, x = 1, y = 2, z = 3.

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Matrices

Using matrices, solve the following system of equations:
2x – 3y + 5 = 11
3x + 2y – 4z = -5
x + y – 2z= -3

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NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

Matrices

Using matrices, solve the following system of equations:2x – 3y + 5 = 113x + 2y – 4z = -5x + y – 2z= -3

Some More Questions From Matrices Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Using matrices, solve the following system of equations:
2x – 3y + 5 = 11
3x + 2y – 4z = -5
x + y – 2z= -3