QuestionIf possible, find , and . (If not possible, enter IMPOSSIBLE in any cell of the matrix.) (a) (b) (c) (d)
Studdy Solution
STEP 1
1. Matrix addition and subtraction require matrices of the same dimensions.
2. Scalar multiplication can be performed on any matrix.
3. The given matrices and have dimensions and , respectively.
STEP 2
1. Determine if is possible.
2. Determine if is possible.
3. Calculate .
4. Determine if is possible.
STEP 3
To add matrices and , they must have the same dimensions. Matrix is and matrix is . Since they do not have the same dimensions, is not possible.
Result for : IMPOSSIBLE
STEP 4
To subtract matrices and , they must have the same dimensions. Matrix is and matrix is . Since they do not have the same dimensions, is not possible.
Result for : IMPOSSIBLE
STEP 5
To calculate , multiply each element of matrix by 3:
\[
3A = 3 \times \begin{bmatrix}
7 & 0 & 3 \\
-4 & -2 & 0
\end{bmatrix}
= \begin{bmatrix}
3 \times 7 & 3 \times 0 & 3 \times 3 \\
3 \times (-4) & 3 \times (-2) & 3 \times 0
\end{bmatrix}
= \begin{bmatrix}
21 & 0 & 9 \\
-12 & -6 & 0
\end{bmatrix}$
STEP 6
To calculate , both matrices must have the same dimensions. Since is and is , they do not have the same dimensions, and is not possible.
Result for : IMPOSSIBLE
The results are:
(a) : IMPOSSIBLE
(b) : IMPOSSIBLE
(c) :
(d) : IMPOSSIBLE
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