Repeat

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

Repeat

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Take

A = A I

[\begin{array}{ccc} 1 & a m p; 3 & a m p; 3 \\ 1 & a m p; 4 & a m p; 3 \\ 1 & a m p; 3 & a m p; 4 \end{array}] = A [\begin{array}{ccc} 1 & a m p; 0 & a m p; 0 \\ 0 & a m p; 1 & a m p; 0 \\ 0 & a m p; 0 & a m p; 1 \end{array}]

c_{2} \to c_{2} - 3 c_{1}

and

c_{3} \to c_{3} - 3 c_{1}

[\begin{array}{ccc} 1 & a m p; 0 & a m p; 0 \\ 1 & a m p; 1 & a m p; 0 \\ 1 & a m p; 0 & a m p; 1 \end{array}] = A [\begin{array}{ccc} 1 & a m p; - 3 & a m p; - 3 \\ 0 & a m p; 1 & a m p; 0 \\ 0 & a m p; 0 & a m p; 1 \end{array}]

c_{1} \to c_{1} - c_{2}

[\begin{array}{ccc} 1 & a m p; 0 & a m p; 0 \\ 0 & a m p; 1 & a m p; 0 \\ 1 & a m p; 0 & a m p; 1 \end{array}] = A [\begin{array}{ccc} 4 & a m p; - 3 & a m p; - 3 \\ - 1 & a m p; 1 & a m p; 0 \\ 0 & a m p; 0 & a m p; 1 \end{array}]

c_{1} \to c_{1} - c_{3}

[\begin{array}{ccc} 1 & a m p; 0 & a m p; 0 \\ 0 & a m p; 1 & a m p; 0 \\ 0 & a m p; 0 & a m p; 1 \end{array}] = A [\begin{array}{ccc} 7 & a m p; - 3 & a m p; - 3 \\ - 1 & a m p; 0 & a m p; 0 \\ - 1 & a m p; 0 & a m p; 1 \end{array}]

∴ A^{- 1} = [\begin{array}{ccc} 7 & a m p; - 3 & a m p; - 3 \\ - 1 & a m p; 0 & a m p; 0 \\ - 1 & a m p; 0 & a m p; 1 \end{array}]