PJJ@USM 101 : Matrix Multiplication

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Topic 1.3 Matrix Multiplication	SLT
Get YouTube Transcripts Video Please watch the video on Matrix Multiplication.	8 mins
Notes Please download and read Notes 1.3	10 mins
Activity 1.1 Please complete Activity 1.3	30 mins

Activity 1.3

Let's go through an example of matrix multiplication.

Consider matrices

A = [\begin{array}{cc} 2 & - 1 \\ 3 & 4 \end{array}]

B = [\begin{array}{cc} 1 & 3 \\ - 2 & 0 \end{array}]

Question: Find the product

C = A \cdot B

$C_{i j} = \sum_{k-1}^{n} A_{i k} \cdot B_{k j}$

Let's calculate each element of the resulting matrix

C

$C_{11} = (2 \cdot 1) + (- 1 \cdot - 2) = 2 + 2 = 4$

$C_{12} = (2 \cdot 3) + (- 1 \cdot 0) = 6$

$C_{21} = (3 \cdot 1) + (4 \cdot - 2) = 3 - 8 = - 5$

$C_{22} = (3 \cdot 3) + (4 \cdot 0) = 9$

So, the resulting matrix

C

$C = [\begin{array}{cc} 4 & 6 \\ - 5 & 9 \end{array}]$

Therefore,

A \cdot B = [\begin{array}{cc} 4 & 6 \\ - 5 & 9 \end{array}]

Matrix multiplication is not commutative, meaning that

A \cdot B

B \cdot A

If you have any more questions or if there's anything specific you'd like to explore further, feel free to ask!