Lesson Worksheet: Scalar Multiplication of Matrices Mathematics • 10th Grade

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In this worksheet, we will practice multiplying a scalar by a matrix and identifying the properties of their multiplication.

Q1:

Given that A=⟨−1,−8⟩, find 3A.

  • A⟨−1,−24⟩
  • B⟨−24,−3⟩
  • C⟨−3,−24⟩
  • D⟨−3,−8⟩

Q2:

If 𝐴=[8−31], what is 0𝐴?

  • A[000]
  • B[0−30]
  • C[001]
  • D[8−31]
  • E0

Q3:

Given that 𝑥×−20−3−5=1402135, find the value of 𝑥.

Q4:

True or False: The multiplication of a matrix by a scalar is distributive with respect to matrix addition, that is, 𝛼(𝐴+𝐵)=𝛼𝐴+𝛼𝐵 for any scalar 𝛼 and any matrices 𝐴 and 𝐵 such that their addition is defined.

  • AFalse
  • BTrue

Q5:

True or False: Since the scalar multiplication of a zero matrix produces a zero matrix, it follows that 𝑐⋅𝑂=𝑂, where 𝑐 is a scalar and 𝑂 is a zero matrix.

  • AFalse
  • BTrue

Q6:

True or False: The multiplication of a matrix by a scalar is associative, that is, 𝛼𝛽𝐴=𝛼(𝛽𝐴)=(𝛼𝛽)𝐴 for any matrix 𝐴 and any scalars 𝛼 and 𝛽.

  • AFalse
  • BTrue

Q7:

Given the matrix 𝐴=01−3−101,

what is −6𝐴?

  • A0−61860−1
  • B06−18−606
  • C0−61860−6
  • D0−6−3−10−6
  • E06−18−601

Q8:

Consider the matrix equation 819−3=𝑚302−1+−1130, Find the value of 𝑚 that solves this equation.

Q9:

Given the matrix 𝐴=1−1652−4−3−174, what is the greatest number 𝑘 for which no entry of 𝑘𝐴 is greater than 1?

  • A−17
  • B125
  • C17
  • D116
  • E−116

Q10:

Find numbers 𝑎, 𝑏, and 𝑐 so that 𝑎110−1+𝑏1001+𝑐0−110=10−13.

  • A𝑎=−1, 𝑏=3, 𝑐=−1
  • B𝑎=1, 𝑏=2, 𝑐=1
  • C𝑎=1, 𝑏=−2, 𝑐=1
  • D𝑎=1, 𝑏=3, 𝑐=1
  • E𝑎=−1, 𝑏=2, 𝑐=−1

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