Properties of matrices — A/L Combined Mathematics

How do I practise Properties of matrices?

1 question with a worked solution

Check before you answer: Order Compatibility Check: Verifying dimension compatibility before attempting matrix multiplication.

1. If matrix A has dimension 3 × 2 and matrix B has dimension 2 × 4, what is the dimension of the product matrix AB?
   1. A) Multiplication is not defined
   2. B) 3 × 4
   3. C) 4 × 3
   4. D) 2 × 2
   Check my answer

   Correct answer: B) 3 × 4

   Matrix multiplication AB is defined because the number of columns of A (2) equals the number of rows of B (2). The resulting product matrix takes the number of rows of A and the number of columns of B, giving dimension 3 × 4.

   Show worked solution

   Step 1: Check compatibility: (3 × 2) · (2 × 4) -> inner dimensions match (2 = 2). Step 2: Product dimension = outer dimensions = 3 × 4. Answer: 3 × 4.
   Modelled on: the A/L Combined Mathematics examination pattern

Get this auto-marked

Next in the syllabus

Where does Properties of matrices fit in the syllabus?

Year 2 · Term 1