Question
If \( A \) is a \( 6 \times 4 \) matrix and the sum \( A+B \) can be computed, what is the size of \( B \) ?
Ask by Ball Tucker. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Matrix B must be a 6×4 matrix.
Solution
For the sum A + B to be defined, the two matrices must have the same dimensions. Since A is a 6×4 matrix, B must also be a 6×4 matrix.
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Simplify this solution Beyond the Answer
To determine the size of matrix \( B \), we need to recall the rule for matrix addition: two matrices can be added together if and only if they have the same dimensions. Since matrix \( A \) is a \( 6 \times 4 \) matrix (which means it has 6 rows and 4 columns), matrix \( B \) must also have 6 rows and 4 columns in order for the sum \( A + B \) to be computable. Therefore, the size of \( B \) must be \( 6 \times 4 \) as well.
