Practice the problems given in the worksheet on addition of matrices.
If M and N are the two matrices of the same order, then the matrices are said conformable for addition, and their sum is obtained by adding the corresponding elements of M and N.
1. Find the sum of A and B where A = \(\begin{bmatrix} 2 & 3\\ -5 & 7 \end{bmatrix}\) and B = \(\begin{bmatrix} 4 & 6\\ 2 & -11 \end{bmatrix}\)
2. Find A + B when A = \(\begin{bmatrix} 2 & 3 & 4\\ 5 & 6 & 7\\ 8 & 5 & 11 \end{bmatrix}\) and B = \(\begin{bmatrix} 3 & -2 & -3\\ 5 & 4 & 3\\ 1 & 3 & 2 \end{bmatrix}\)
3. If A = \(\begin{bmatrix} -1 & 2 & -3\\ -2 & 1 & 4 \end{bmatrix}\) and B = \(\begin{bmatrix} 0 & -1 & 2\\ 3 & 0 & 1 \end{bmatrix}\), then find the sum of A and B.
4. If \(\begin{bmatrix} 2 & 3\\ -5 & 4 \end{bmatrix}\) + \(\begin{bmatrix} -2 & 1\\ x & 3\end{bmatrix}\) = \(\begin{bmatrix} 0 & 4\\ -3 & 9 \end{bmatrix}\), find the value of x.
5. Given A = \(\begin{bmatrix} 1 & 4\\ 2 & 3 \end{bmatrix}\) and B = \(\begin{bmatrix} -4 & -1\\ -3 & -2 \end{bmatrix}\), compute A + B.
6. If \(\begin{bmatrix} 5 & -3\\ 2 & 4 \end{bmatrix}\) + A = \(\begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix}\), find the matrix A.
7. Given M = \(\begin{bmatrix} 1 & 3\\ 2 & 4 \end{bmatrix}\), find a matrix N such that M + N = \(\begin{bmatrix} 0 & 0\\ 0 & 0 \end{bmatrix}\).
8. If A = \(\begin{bmatrix} 1 & 0 & 2\\ 0 & 2 & 3\\ 1 & 0 & 0 \end{bmatrix}\), B = \(\begin{bmatrix} 0 & -1 & 0\\ -2 & 0 & 3\\ 0 & 1 & 2 \end{bmatrix}\) and C = \(\begin{bmatrix} 2 & 3 & 1\\ 0 & 0 & -3\\ 1 & 1 & -1 \end{bmatrix}\), find A + B + C.
Answers for the worksheet on addition of matrices are given below.
Answers:
1. \(\begin{bmatrix} 6 & 9\\ -3 & -4 \end{bmatrix}\)
2. \(\begin{bmatrix} 5 & 1 & 1\\ 10 & 10 & 10\\ 9 & 8 & 13 \end{bmatrix}\)
3. \(\begin{bmatrix} -1 & 1 & -1\\ 1 & 1 & 5 \end{bmatrix}\)
4. x = 2
5. \(\begin{bmatrix} -3 & 3\\ -1 & 1 \end{bmatrix}\)
6. \(\begin{bmatrix} -4 & 3\\ -2 & -3 \end{bmatrix}\)
7. \(\begin{bmatrix} -1 & -3\\ -2 & -4 \end{bmatrix}\)
8. \(\begin{bmatrix} 3 & 2 & 3\\ -2 & 2 & 3\\ 2 & 2 & 1 \end{bmatrix}\)
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