Matrix Multiplication (VCE SSCE General Mathematics): Quizzes

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Matrix Multiplication
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For matrices AA (order 4×34 \times 3) and BB (order 3×23 \times 2), is ABAB defined?

Yes, the inner numbers match (both 3)

What is the order of ABAB if AA is 5×25 \times 2 and BB is 2×42 \times 4?

5×45 \times 4

What is [23][45]\begin{bmatrix} 2 & 3 \end{bmatrix} \begin{bmatrix} 4 \\ 5 \end{bmatrix}?

2323

Matrix multiplication is not commutative. What does this mean?

ABBAAB \neq BA generally

Which matrix is the 2×22 \times 2 identity matrix II?

[1001]\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}

For any matrix AA, what is AIAI where II is the identity matrix?

AA

What does A3A^3 mean for a matrix AA?

A×A×AA \times A \times A

Why can only square matrices be raised to powers?

Need matching dimensions to multiply by itself

If ABAB is defined for AA (3×23 \times 2) and BB (2×52 \times 5), is BABA defined?

No, inner numbers are 55 and 33

Books cost 20 USD, puzzles 30 USD. If sold [74]\begin{bmatrix} 7 & 4 \end{bmatrix}, what's the total?

260 USD

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