USING ELEMENTARY TRANSFORMATIONS,FIND THE INVERSE OF EACH OF THE MATRICES,IF IT EXISTS [1 3 -2 -3 0 -5 2 5 - Maths - Matrices

Question

USING ELEMENTARY TRANSFORMATIONS,FIND THE INVERSE OF EACH OF THE
MATRICES,IF IT EXISTS
[1 3 -2
-3 0 -5
2 5 0]
PLEASE DESCRIBE IN EASY & GIVES A TRICK & TEACHNIQUETO
EASY WAY TO FIND OUT IN 5 MINUTES

Shridhar Kaushik · Accepted Answer

We have â€“ A = I A $\Rightarrow [\begin{matrix} 1 & 3 & - 2 \\ - 3 & 0 & - 5 \\ 2 & 5 & 0 \end{matrix}] = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}] A {Applying R}_{2} \to R_{2} + 3 R_{1} {and R}_{3} \to R_{3} - 2 R_{1},$ We get â€“ $[\begin{matrix} 1 & 3 & - 2 \\ 0 & 9 & - 11 \\ 0 & - 1 & 4 \end{matrix}] = [\begin{matrix} 1 & 0 & 0 \\ 3 & 1 & 0 \\ - 2 & 0 & 1 \end{matrix}] A R_{2} \to R_{2} + 8 R_{3}, We get - [\begin{matrix} 1 & 3 & - 2 \\ 0 & 1 & 21 \\ 0 & - 1 & 4 \end{matrix}] = [\begin{matrix} 1 & 0 & 0 \\ - 13 & 1 & 8 \\ - 2 & 0 & 1 \end{matrix}] A R_{3} \to R_{3} + R_{2}, We get - [\begin{matrix} 1 & 3 & - 2 \\ 0 & 1 & 21 \\ 0 & 0 & 25 \end{matrix}] = [\begin{matrix} 1 & 0 & 0 \\ - 13 & 1 & 8 \\ - 15 & 1 & 9 \end{matrix}] A$ $R_{1} \to R_{1} - 3 R_{2}, We get - [\begin{matrix} 1 & 0 & - 65 \\ 0 & 1 & 21 \\ 0 & 0 & 25 \end{matrix}] = [\begin{matrix} 40 & - 3 & - 24 \\ - 13 & 1 & 8 \\ - 15 & 1 & 9 \end{matrix}] A R_{3} \to \frac{1}{25} R_{3}, we get - [\begin{matrix} 1 & 0 & - 65 \\ 0 & 1 & 21 \\ 0 & 0 & 1 \end{matrix}] = [\begin{matrix} 40 & - 3 & - 24 \\ - 13 & 1 & 8 \\ \frac{- 15}{25} & \frac{1}{25} & \frac{9}{25} \end{matrix}] A R_{2} \to R_{2} - 21 R_{3}, R_{1} \to R_{1} + 65 R_{3}, we get -$ $[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}] = [\begin{matrix} 1 & \frac{- 2}{5} & \frac{- 3}{5} \\ \frac{- 2}{5} & \frac{4}{25} & \frac{11}{25} \\ \frac{- 15}{25} & \frac{1}{25} & \frac{9}{25} \end{matrix}] A$ Hence, the inverse of matrix A is â€“ $A^{- 1} = [\begin{matrix} 1 & \frac{- 2}{5} & \frac{- 3}{5} \\ \frac{- 2}{5} & \frac{4}{25} & \frac{11}{25} \\ \frac{- 15}{25} & \frac{1}{25} & \frac{9}{25} \end{matrix}]$

USING ELEMENTARY TRANSFORMATIONS,FIND THE INVERSE OF EACH OF THE MATRICES,IF IT EXISTS [1 3 -2 -3 0 -5 2 5 0] PLEASE DESCRIBE IN EASY & GIVES A TRICK & TEACHNIQUETO EASY WAY TO FIND OUT.IN 5 MINUTES......

USING ELEMENTARY TRANSFORMATIONS,FIND THE INVERSE OF EACH OF THE MATRICES,IF IT EXISTS

[1 3 -2

-3 0 -5

2 5 0]

PLEASE DESCRIBE IN EASY & GIVES A TRICK & TEACHNIQUETO EASY WAY TO FIND OUT.IN 5 MINUTES......