Worksheet: Matrix Operations

In this worksheet, we will practice performing operations on matrices, such as adding them, subtracting them, transposing them, and multiplying them by scalars.

Q1:

Solve for matrix 𝑋 in the matrix equation 3 𝑋 + 𝐵 = 𝐶 , where 𝐵 and 𝐶 are

  • A 1 3 4 5
  • B 3 9 1 2 1 5
  • C 0 1 2 1 1 4
  • D 1 3 4 5
  • E 6 6 1 5 1 8

Q2:

Find the sum of the following matrices.

  • A 1 8 7 3 2
  • B 1 8 4 1 4 8
  • C 2 1 1 0 1 0 8
  • D 1 8 1 0 0 8
  • E 1 8 1 0 6 8

Q3:

Given that what is 1 3 ( 𝐴 + 𝐵 ) ?

  • A 2 4 4 3 4 3
  • B 6 5 3 4
  • C 6 1 2 4 4
  • D 2 5 3 1 4 3

Q4:

Given that find 𝐴 𝑇 .

  • A 6 4 6 8 2 1
  • B 1 2 8 6 4 6
  • C 1 8 4 2 6 6
  • D 2 1 6 8 6 4

Q5:

If and , is ?

  • Ayes
  • Bno

Q6:

Suppose that , , and .

Find .

  • A
  • B
  • C
  • D
  • E

Find .

  • A
  • B
  • C
  • D
  • E

Find .

  • A
  • B
  • C
  • D
  • E

Express in terms of and .

  • A
  • B
  • C
  • D
  • E

Q7:

Consider the matrices

Find 𝐴 + 𝐵 𝐴 𝐵 𝑇 𝑇 .

  • A 8 0 8 7 8 3 2
  • B 4 2 4 7 2 5 2
  • C 8 0 7 8 8 3 2
  • D 4 7 2 2 4 5 2
  • E 6 8 5 4 2 4 2 0

Q8:

Given that determine 𝐴 𝐵 𝑇 𝑇 .

  • A 1 8 2 2 3 4 3 3
  • B 1 7 4 0 2 0 3 8
  • C 1 8 1 0 1 0 3
  • D 1 7 2 0 4 0 3 8

Q9:

Given that determine the matrix 𝐵 .

  • A 8 1 2 5 6 5 4 1 1 6 1
  • B 8 6 1 1 1 2 5 6 5 4 1
  • C 8 1 1 6 5 5 1 1 0 3 1
  • D 8 5 1 0 1 1 5 3 6 1 1

Q10:

Given that find the result of 𝐴 𝐵 𝑇 , if possible.

  • A 1 4 1 0 2 4 6 1 2
  • BIt is not possible.
  • C 1 4 2 6 1 0 4 1 2
  • D 1 4 2 6 1 0 4 1 2
  • E 1 4 1 0 2 4 6 1 2

Q11:

If and then which of the following cannot exist?

  • A
  • B
  • C
  • D

Q12:

Given that the order of the matrix 𝐴 is 2 × 2 , and that of the matrix 𝐵 𝑇 is 1 × 2 , which of the following operations can be performed?

  • A 𝐴 + 𝐵 𝑇 𝑇
  • B 𝐴 + 𝐵
  • C 𝐴 × 𝐵 𝑇
  • D 𝐴 × 𝐵

Q13:

𝐽 and 𝐾 are two matrices with the property that for any 3 × 3 matrix 𝑋 , 𝐽 𝑋 = 𝑋 and 𝑋 𝐾 = 𝑋 . Are 𝐽 and 𝐾 equal?

  • A No, they are different matrices of the same dimensions.
  • B No, they have different dimensions.
  • C Yes, they are both the 3 × 3 identity matrix.

Q14:

𝐽 and 𝐾 are two matrices with the property that for any 2 × 3 matrix 𝑋 , 𝐽 𝑋 = 𝑋 and 𝑋 𝐾 = 𝑋 . Are 𝐽 and 𝐾 equal?

  • A No, they are different matrices of the same dimensions.
  • B Yes, they are both the identity matrix.
  • C No, they have different dimensions.

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