For the following matrices, verify that A(BC) = (AB)C: and C = [1

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

For the following matrices, verify that A(BC) = (AB)C:
$A = [\begin{array}{ccc} 2 & 3 & - 1 \\ 3 & 0 & 2 \end{array}], B = [\begin{array}{c} 1 \\ 1 \\ 2 \end{array}]$ and C = [1 – 2]

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

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

$A = [\begin{array}{ccc} 2 & 3 & - 1 \\ 3 & 0 & 2 \end{array}] B = [\begin{array}{l} 1 \\ 1 \\ 2 \end{array}] C = [\begin{array}{ll} 1 - 2 \end{array}]$

$BC = [\begin{array}{l} 1 \\ 1 \\ 2 \end{array}] [\begin{array}{ll} 1 - 2 \end{array}] = [\begin{array}{ll} 1 - 2 \\ 1 - 2 \\ 2 - 4 \end{array}] = [\begin{array}{l} - 1 \\ - 1 \\ - 2 \end{array}]$

$A \cdot (BC) = [\begin{array}{ccc} 2 & 3 & - 1 \\ 3 & 0 & 2 \end{array}] [\begin{array}{l} - 1 \\ - 1 \\ - 2 \end{array}] = [\begin{array}{l} - 2 - 3 + 2 \\ - 3 + 0 - 4 \end{array}] = [\begin{array}{l} - 3 \\ - 7 \end{array}]$

Now, $AB = [\begin{array}{ccc} 2 & 3 & - 1 \\ 3 & 0 & 2 \end{array}] [\begin{array}{l} 1 \\ 1 \\ 2 \end{array}] = [\begin{array}{l} 2 + 3 - 2 \\ 3 + 0 + 4 \end{array}] = [\begin{array}{l} 3 \\ 7 \end{array}]$

$∴ (AB) C = [\begin{array}{l} 3 \\ 7 \end{array}] [\begin{array}{ll} - 1 - 2 \end{array}] = [\begin{array}{l} - 3 - 6 \\ - 7 - 14 \end{array}] = [\begin{array}{l} - 9 \\ - 21 \end{array}]$

$= [\begin{array}{l} - 3 \\ - 7 \end{array}]$

∴ A(BC) = (AB)C

Please subscribe our Youtube channel to unlock this solution.