Transcript Boardworks Matrices free resources

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What is a matrix?
A matrix (plural matrices) is a rectangular array of numbers,
displayed in rows and columns inside a large set of brackets.
One use of matrices is to organise data clearly.
For example, the number of people that attended an
exhibition over one weekend can be arranged in a matrix.
Saturday Sunday
Men
129
105
Women
103
99
Children
80
67
129
105
103
99
80
67
This is a 3 × 2 (“3 by 2”) matrix because it has 3 rows and
2 columns. It contains 6 elements or entries.
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Adding matrices
Two matrices can be added or subtracted if they have the
same dimensions.
Add each corresponding element from both matrices to get
the resulting element.
6
For example:
5
–2 13
8 –17
+
12
4
1
–3
2
0
=
6 + 12
5+4
–2 + 1
13 – 3
8+2
–17 + 0
18
=
9
–1 10
10 –17
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Adding and subtracting matrices
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Multiplying by a scalar
A matrix can be multiplied by a single value (a scalar).
Simply multiply each entry in the matrix by that scalar to get
the resulting matrix.
For example:
Calculate: 5
=
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3
7
5
3
2
11
1
3
2
11
1
15 10
55
5
–
–
=
7×3
5×3
3×3
2×3
11 × 3
1×3
1
2
3
2
1
2
3
2
=
21 15
=
14
8
52
3
9
6
33
3
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Multiplying two matrices
Two matrices A and B can be multiplied, but only if the number
of columns in matrix A equals the number of rows in matrix B.
An m × n matrix can be multiplied by an n × p matrix,
and the result is an m × p matrix.
Unlike with numbers, the order in which two matrices are
multiplied does matter, i.e. AB ≠ BA as a rule.
List all possible product pairs from the matrices below.
A=
12
7
5
7
3
3
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B=
12
13
15
9
1
C=
4
D=
129
103
7
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How to multiply two matrices
To multiply two matrices, perform the dot product on rows
and columns of the matrices.
The dot product is the sum of the product of the corresponding
entries.
For example:
1
2
3
4
=
(1 × 4) + (2 × 5) + (3 × 6)
=
4 + 10 + 18
5
6
=
32
For larger matrices, start with the first row of the first matrix
and perform the dot product on each column of the second.
Work through each row of the first matrix in this way.
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Multiplying two matrices
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