Worksheet: Matrix Operations

In this worksheet, we will practice combining the operations of addition, subtraction, scalar multiplication, and transposing matrices.

Q1:

Solve for matrix 𝑋 in the matrix equation 3𝑋+𝐵=𝐶, where 𝐵 and 𝐶 are 𝐵=57108,𝐶=8227.

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

Q2:

Given that 𝐴=7542𝐵=1072,, what is 13(𝐴+𝐵)?

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

Q3:

Given that both 𝐴 and 𝐵 have the order 1×2, determine the order of the matrix 6𝐴6𝐵.

  • A 1 × 2
  • B 2 × 1
  • C 6 × 1 2
  • D 6 × 6

Q4:

Consider the matrices 𝑍=7411,𝐴=7433. Is it true that 7(𝑍+𝐴)=7(𝐴)7(𝑍)?

  • Ayes
  • Bno

Q5:

Given that 𝑋=321588𝑌=189972𝑍=387085,,, what is the matrix 3𝑋+𝑌3𝑍?

  • A 1 2 2 2 7 6 4 1 1 1
  • B 1 9 1 1 5 3 7 4
  • C 0 1 1 4 3 8 4
  • D 1 9 2 6 1 5 6 7 4 1

Q6:

Given that 𝐵=1373𝐵𝐵=𝐴,, determine the value of 𝑎+𝑎.

  • A0
  • B 2 0
  • C8
  • D20

Q7:

If the matrices 𝐴 and 𝐵 both have order 𝑚×𝑛, then what is the order of the matrix 𝐴2𝐵?

  • A 𝑛 × 𝑚
  • B 1 × 𝑛
  • C 𝑚 × 𝑛
  • D 𝑚 × 1

Q8:

If 𝐴 is a 2×3 matrix and 𝐵 is a 3×2 matrix, can you add the matrices 𝐴 and 𝐵?

  • ANo
  • BYes

Q9:

If the matrix 𝐴 is added to a zero matrix of the same size, is the result equal to matrix 𝐴?

  • AYes
  • BNo

Q10:

Complete the following.

If 𝐴 and 𝐵 are two matrices with the same size, then 𝐴+𝐵=.

  • A 𝐵 𝐴
  • B 𝐴 𝐵
  • C 𝐴 + 𝐵
  • D 𝐴 + 𝐵
  • E 𝐴 𝐵

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