Question

If A =[1,2,4,3], find B such that A+B=0

Matrix transformations
ANSWERED
asked 2021-02-14

If \(A =[1,2,4,3]\), find B such that \(A+B=0\)

Answers (1)

2021-02-15

Recall: Theorem: The matrix addition is associative that is let A,B,C be matrices of order M x n. Then, \((A+B)+C=A+(B+C)\).
Theorem: The matrix addition is commutative that is let A and B be matrices of order M x n. Then \(A+B=B+A\).
The given matrix is, \(A=[1,2,4,3]\).
We have to find a matrix B such that \(A+B=0\), where 0 is the zero matrix. Now,
\(A+B=0\)
\(\displaystyle\to{B}+{A}={0}\)
\(\displaystyle\to{\left({B}+{A}\right)}-{A}={0}-{A}\)
\(\displaystyle\to{B}+{\left({A}-{A}\right)}=-{A}\)
\(\displaystyle\to{B}+{0}=-{A}\)
\(\displaystyle\to{B}=-{A}\)
\(\displaystyle\to{B}=-{\left[{1},{2},{4},{3}\right]}\)
\(\rightarrow B=[-1,-2,-4,-3]\)
Therefore, when \(A=[1,2,4,3]\), for \(B=[-1,-2,-4,-3], A+B=0\).

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