QuestionIf possible, find . (If not possible, enter IMPOSSIBLE in any cell of the matrix.)
State the dimension of the result. (If not possible, enter IMPOSSIBLE in both answer blanks.)
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STEP 1
1. Matrix multiplication is only possible when the number of columns in the first matrix equals the number of rows in the second matrix.
2. The result of matrix multiplication will have dimensions equal to the number of rows of the first matrix by the number of columns of the second matrix.
STEP 2
1. Determine the dimensions of matrices and .
2. Check if matrix multiplication is possible.
3. If possible, calculate the product .
4. State the dimensions of the resulting matrix.
STEP 3
Determine the dimensions of matrices and .
Matrix is a matrix.
Matrix is a matrix.
STEP 4
Check if matrix multiplication is possible.
Matrix multiplication is possible if the number of columns in (which is 2) is equal to the number of rows in (which is 2).
Since both are equal, matrix multiplication is possible.
STEP 5
Calculate the product .
The resulting matrix will have dimensions .
Calculate each element of the resulting matrix:
STEP 6
State the dimensions of the resulting matrix.
The dimensions of the resulting matrix are .
The resulting matrix is:
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