UPSKILL MATH PLUS

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We can multiply the elements of the given matrix $$A$$ by a non-zero number $$k$$ to obtain a new matrix $$kA$$ whose elements are multiplied by $$k$$.

The matrix $$kA$$ is called the scalar multiplication of $$A$$.

If $$A = (a_{ij})_{m×n}$$,  then, $$kA = (ka_{ij})_{m×n}$$ for all $$i = 1, 2,...m$$, and such that $$j = 1, 2, ….n$$
Example:
Determine 5$$A + B$$, if $$A =\begin{bmatrix} 2 & 4 & 6\\ 7 & 5 & -4\\ -2 & 1 & 7 \end{bmatrix}, B = \begin{bmatrix} 2 & 4 & 6\\ 7 & 5 & 3\\ 7 & 1 & 7 \end{bmatrix}$$

Both the matrices $$A$$ and $$B$$ have same orders as $$3 × 3$$, so 5$$A + B$$ is defined.

Therefore, we have 5$$A + B = 5\begin{bmatrix} 2 & 4 & 6\\ 7 & 5 & -4\\ -2 & 1 & 7 \end{bmatrix} + \begin{bmatrix} 2 & 4 & 6\\ 7 & 5 & 3\\ 7 & 1 & 7 \end{bmatrix}$$

$$= \begin{bmatrix} 2 × 5 & 4 × 5 & 6 × 5\\ 7 × 5 & 5 × 5& -4 × 5\\ -2 × 5 & 1 × 5 & 7 × 5 \end{bmatrix} + \begin{bmatrix} 2 & 4 & 6\\ 7 & 5 & 3\\ 7 & 1 & 7 \end{bmatrix}$$

$$= \begin{bmatrix} 10 & 20 & 30 \\ 25 & 20 & -20\\ -10 & 5 & 35 \end{bmatrix} + \begin{bmatrix} 2 & 4 & 6\\ 7 & 5 & 3\\ 7 & 1 & 7 \end{bmatrix}$$

Now we add the two matrices.

$$= \begin{bmatrix} 12 & 24 & 36 \\ 32 & 25 & -17\\ -3 & 6 & 42 \end{bmatrix}$$