If , find matrix C such that A + B + C = 0, where O is the zero matrix.

Engineering

Mathematics

Algebra of Matrices

Question

If $A = [\begin{array}{cc} 2 & 2 \\ - 3 & 1 \\ 4 & 0 \end{array}], B = [\begin{array}{cc} 6 & 2 \\ 1 & 3 \\ 0 & 4 \end{array}]$ , find matrix C such that A + B + C = 0, where O is the zero matrix.

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

$A = [\begin{array}{cc} 2 & 2 \\ - 3 & 1 \\ 4 & 0 \end{array}] B = [\begin{array}{cc} 6 & 2 \\ 1 & 3 \\ 0 & 4 \end{array}]$

A + B + C = 0

[\begin{array}{cc} 6 & 2 \\ 1 & 3 \\ 0 & 4 \end{array}] + [\begin{array}{cc} 2 & 2 \\ - 3 & 1 \\ 4 & 0 \end{array}] + C = [\begin{array}{cc} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}]

[\begin{array}{cc} 6 + 2 & 2 + 2 \\ 1 - 3 & 3 + 1 \\ 0 + 4 & 4 + 0 \end{array}] + C = [\begin{array}{cc} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}]

[\begin{array}{cc} 8 & 4 \\ - 2 & 4 \\ 4 & 4 \end{array}] + C = [\begin{array}{cc} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}]

C = [\begin{array}{cc} - 8 & - 4 \\ 2 & - 4 \\ - 4 & - 4 \end{array}]