Exercise · ZW-MATRIX-MULTIPLICATION-003 · ★☆☆ Basic
Let \(A\) be \(3\times 4\) and \(B\) be \(4\times 2\). Which product is defined?
Choose one option.
Show answer
- A. \(AB\), of size \(3\times 2\)
Explanation
\(AB\) exists because the columns of \(A\) (4) match the rows of \(B\) (4). For \(BA\) we would compare 2 columns with 3 rows, which differ.
Review the concept: Matrix multiplication
The product \(AB\) of two matrices \(A\) and \(B\), when \(A\) has as many columns as \(B\) has rows, is the matrix whose \((i,j)\) entry combines row \(i\) of \(A\) with column \(j\) of \(B\).
\[(AB)_{ij}=\sum_{k=1}^{n}a_{ik}b_{kj}\]
More practice problems: matrix multiplication
- ZW-MATRIX-MULTIPLICATION-001 If A is 2× 3 and B is 3× 4, what is the size of AB?
- ZW-MATRIX-MULTIPLICATION-002 Compute AB for A=[1 2; 3 4] and B=[0 1; 1 0].
- ZW-MATRIX-MULTIPLICATION-004 For A=[2 -1; 0 3] and B=[1 4; 5 2], what is the entry (AB)_21?
- ZW-MATRIX-MULTIPLICATION-005 For A=[1 1; 0 1] and B=[1 0; 1 1], compute AB-BA.
- ZW-MATRIX-MULTIPLICATION-006 If I is the 2× 2 identity and A=[3 -2; 1 5], what is AI?
- ZW-MATRIX-MULTIPLICATION-007 Compute Amathbf v for A=[1 2 0; 0 1 -1] and mathbf v=[2; 1; 3].
- ZW-MATRIX-MULTIPLICATION-008 Which of these equalities holds for matrices A,B,C whose products are defined?
- ZW-MATRIX-MULTIPLICATION-009 Compute A^2 for A=[1 1; 1 0].
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