Find the value of p and q such that A2 + pl = qA, where

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

Find the value of p and q such that A² + pl = qA, where $A = [\begin{array}{cc} 3 & 1 \\ 7 & 5 \end{array}]$

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

$A^{2} = [\begin{array}{ll} 3 1 \\ 7 5 \end{array}] [\begin{array}{ll} 3 1 \\ 7 5 \end{array}] = [\begin{array}{ll} 9 + 7 3 + 5 \\ 21 + 35 7 + 25 \end{array}]$

$A^{2} = [\begin{array}{ll} 16 8 \\ 56 32 \end{array}]$

A² + pl = qA

$\Rightarrow [\begin{array}{cc} 16 & 8 \\ 56 & 32 \end{array}] + [\begin{array}{cc} p & 0 \\ 0 & p \end{array}] = [\begin{array}{ll} 3 q q \\ 7 q 5 q \end{array}]$

$\Rightarrow [\begin{array}{cc} 16 + p & 8 \\ 56 & 32 + p \end{array}] = [\begin{array}{cc} 3 q & q \\ 7 q & 5 q \end{array}]$

8 = q so 16 lp = 3q

16 lp = 24

p = 8

so p = 8 & q = 8

Please subscribe our Youtube channel to unlock this solution.