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=57−10−8,𝐶=8−227.

  • A3−91215
  • B6−61518
  • C−13−4−5
  • D1−345
  • E0−12−11−4

Q2:

Given that 𝐴=−75−4−2𝐵=107−2,, what is 13(𝐴+𝐵)?

  • A−24−43−43
  • B−612−4−4
  • C−653−4
  • D⎡⎢⎢⎣−2531−43⎤⎥⎥⎦

Q3:

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

  • A1×2
  • B2×1
  • C6×12
  • D6×6

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−1−22−276−41−11
  • B−19−115−37−4
  • C0−1−14−3−8−4
  • D−19261567−41

Q6:

Given that 𝐵=1−37−3𝐵−𝐵=𝐴,, determine the value of 𝑎+𝑎.

Q7:

If the matrices 𝐴 and 𝐵 both have order 𝑚×𝑛, then what is the order of the matrix 𝐴−2𝐵?

  • A𝑛×𝑚
  • B1×𝑛
  • C𝑚×𝑛
  • D𝑚×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=.

  • A𝐵−𝐴
  • B𝐴−𝐵
  • C𝐴+𝐵
  • D𝐴+𝐵
  • E𝐴−𝐵

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