Matrix Multiplication Worksheet for 11th - 12th Grade | Lesson Planet - Free Printable

Let’s go through each problem one by one. We’re multiplying matrices, and if the multiplication isn’t possible (because the inner dimensions don’t match), we write “undefined”.

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Problem 1a:

Multiply:
[2 -2] × [3 6]
[3 1] [1 -4]

Check dimensions:
First matrix is 2x2, second is 2x2 → multiplication is possible. Result will be 2x2.

Compute:

Row 1, Column 1: (2)(3) + (-2)(1) = 6 - 2 = 4
Row 1, Column 2: (2)(6) + (-2)(-4) = 12 + 8 = 20
Row 2, Column 1: (3)(3) + (1)(1) = 9 + 1 = 10
Row 2, Column 2: (3)(6) + (1)(-4) = 18 - 4 = 14

Result:
[4 20]
[10 14]

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Problem 1b:

Multiply:
[2] × [3 -1 4]
[3]

First matrix is 2x1, second is 1x3 → multiplication is possible. Result will be 2x3.

Compute:

Row 1: (2)(3)=6, (2)(-1)=-2, (2)(4)=8 → [6 -2 8]
Row 2: (3)(3)=9, (3)(-1)=-3, (3)(4)=12 → [9 -3 12]

Result:
[6 -2 8]
[9 -3 12]

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Problem 1c:

Multiply:
[5 -2] × [3 -4]
[0 3] [0 -2]

Both are 2x2 → possible.

Row 1, Col 1: (5)(3) + (-2)(0) = 15 + 0 = 15
Row 1, Col 2: (5)(-4) + (-2)(-2) = -20 + 4 = -16
Row 2, Col 1: (0)(3) + (3)(0) = 0 + 0 = 0
Row 2, Col 2: (0)(-4) + (3)(-2) = 0 - 6 = -6

Result:
[15 -16]
[0 -6]

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Problem 1d:

Multiply:
[2 -3] × [3 -4]
[0 1] [0 -2]

Both 2x2 → possible.

Row 1, Col 1: (2)(3) + (-3)(0) = 6 + 0 = 6
Row 1, Col 2: (2)(-4) + (-3)(-2) = -8 + 6 = -2
Row 2, Col 1: (0)(3) + (1)(0) = 0 + 0 = 0
Row 2, Col 2: (0)(-4) + (1)(-2) = 0 - 2 = -2

Result:
[6 -2]
[0 -2]

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Problem 1e:

Multiply:
[0 -1 2] × [3 -4]
[3 1 0] [0 -2]

First matrix: 2x3, second: 2x2 → inner dimensions: 3 vs 2 → NOT MATCH → UNDEFINED

Answer: undefined

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Problem 1f:

Multiply:
[0 2 4] × [3 -4]
[1 1 0] [0 -2]

First matrix: 2x3, second: 2x2 → inner dimensions: 3 vs 2 → NOT MATCH → UNDEFINED

Answer: undefined

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Problem 1g:

Multiply:
[3] × [3 -1 4]
[1]

First matrix: 2x1, second: 1x3 → possible. Result: 2x3

Row 1: (3)(3)=9, (3)(-1)=-3, (3)(4)=12 → [9 -3 12]
Row 2: (1)(3)=3, (1)(-1)=-1, (1)(4)=4 → [3 -1 4]

Result:
[9 -3 12]
[3 -1 4]

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Problem 1h:

Multiply:
[2 3] × [3 -4]
[2 1] [0 -2]

Both 2x2 → possible.

Row 1, Col 1: (2)(3) + (3)(0) = 6 + 0 = 6
Row 1, Col 2: (2)(-4) + (3)(-2) = -8 -6 = -14
Row 2, Col 1: (2)(3) + (1)(0) = 6 + 0 = 6
Row 2, Col 2: (2)(-4) + (1)(-2) = -8 -2 = -10

Result:
[6 -14]
[6 -10]

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Final Answer:
1a: [4 20]
[10 14]

1b: [6 -2 8]
[9 -3 12]

1c: [15 -16]
[0 -6]

1d: [6 -2]
[0 -2]

1e: undefined

1f: undefined

1g: [9 -3 12]
[3 -1 4]

1h: [6 -14]
[6 -10]