Practice question · Sort into groups
Sort each matrix operation by whether the two matrices must have identical shape.
Groups: Needs identical shape · Does not need identical shape
- Scalar multiple cA
- Addition A + B
- Multiplication A times B
- Subtraction A - B
Hints
- Entry-by-entry operations need matching shapes.
- Multiplication only needs inner dimensions to agree; a scalar multiple involves just one matrix.
Show the answer
Needs identical shape: Addition A + B, Subtraction A - B
Does not need identical shape: Multiplication A times B, Scalar multiple cA
Why
Addition and subtraction act entry by entry, so shapes must match exactly. Multiplication needs only columns-of-A = rows-of-B, and a scalar multiple involves a single matrix, neither needs identical shapes.
Practise Matrices and Matrix Operations
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