9/11/2015
1
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T: +27(0)51 401 9111

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MATM1544
LECTURE 29
Matrix multiplication II
September 11, 2015
T: 051 401 9111
[email protected]
CONTENT
•
Multiplication of matrices
•
Properties of matrix multiplication
•
Alternative notation
•
Transpose of a matrix
•
Zero matrix
•
Identity matrix
•
Examples
•
Exercises
9/11/2015
2
WHEN MAY WE MULTIPLY TWO MATRICES?
We can
only
multiply an
° × ±
matrix with an
± × ²
matrix if
³ ×
±
times
±
× ´
= ³ × ´
Let
µ =
¶
·
¸
¶
¹
¸
…
¶
º
¸
,
» =
¼
·
¼
¹
…
¼
½
,
All vectors with
¾
components each. Then
µ» =
¶
·
¸
¼
·
¶
¹
¸
¼
·
…
¶
º
¸
¼
·
WHEN MAY WE MULTIPLY
We can only multiply an
° × ±
matrix with an
± × ²
matrix.
³ × ¾
times
¾ × ´
= ³ × ´
Let
µ =
¶
·
¸
¶
¹
¸
…
¶
º
¸
,
» =
¼
·
¼
¹
…
¼
½
,
All vectors with
¾
components each. Then
µ» =
¶
·
¸
¼
·
¶
·
¸
¼
¹
¶
¹
¸
¼
·
¶
¹
¸
¼
¹
…
…
¶
º
¸
¼
·
¶
º
¸
¼
¹
9/11/2015
3
WHEN MAY WE MULTIPLY
We can only multiply an
° × ±
matrix with an
± × ²
matrix.
³ × ¾
times
¾ × ´
= ³ × ´
Let
µ =
¶
·
¸
¶
¹
¸
…
¶
º
¸
,
» =
¼
·
¼
¹
…
¼
½
,
All vectors with
¾
components each. Then
µ» =
¶
·
¸
¼
·
¶
·
¸
¼
¹
…
¶
¹
¸
¼
·
¶
¹
¸
¼
¹
…
…
…
…
¶
º
¸
¼
·
¶
º
¸
¼
¹
…
WHEN MAY WE MULTIPLY
We can only multiply an
° × ±
matrix with an
± × ²
matrix.
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 Multiplication, Matrices, Ring, m x n matrix