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

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

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
$$\displaystyle\to{B}+{A}={0}$$
$$\displaystyle\to{\left({B}+{A}\right)}-{A}={0}-{A}$$
$$\displaystyle\to{B}+{\left({A}-{A}\right)}=-{A}$$
$$\displaystyle\to{B}+{0}=-{A}$$
$$\displaystyle\to{B}=-{A}$$
$$\displaystyle\to{B}=-{\left[{1},{2},{4},{3}\right]}$$
PSK->B=[-1,-2,-4,-3]
Therefore, when A=[1,2,4,3], for B=[-1,-2,-4,-3], A+B=0.

### Relevant Questions

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