Worksheet: Matrix Operations

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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=57−10−8,𝐶=8−227.

  • 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=−75−4−2𝐵=107−2,, 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 6𝐴−6𝐵.

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

Q4:

Consider the matrices 𝑍=−74−11,𝐴=7433. Is it true that −7(𝑍+𝐴)=−7(𝐴)−7(𝑍)?

  • Ayes
  • Bno

Q5:

Given that 𝑋=−3−215−8−8𝑌=−18−9−97−2𝑍=3−8−70−85,,, what is the matrix 3𝑋+𝑌−3𝑍?

  • 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=1−37−3𝐵−𝐵=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 𝐴−2𝐵?

  • 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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