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

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.

  • A1,24
  • B24,3
  • C3,24
  • D3,8

Q2:

If 𝐴=[831], what is 0𝐴?

  • A[000]
  • B[030]
  • C[001]
  • D[831]
  • E0

Q3:

Given that 𝑥×2035=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 𝑐𝑂=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=013101,

what is 6𝐴?

  • A0618601
  • B0618606
  • C0618606
  • D063106
  • E0618601

Q8:

Consider the matrix equation 8193=𝑚3021+1130, Find the value of 𝑚 that solves this equation.

Q9:

Given the matrix 𝐴=1165243174, what is the greatest number 𝑘 for which no entry of 𝑘𝐴 is greater than 1?

  • A17
  • B125
  • C17
  • D116
  • E116

Q10:

Find numbers 𝑎, 𝑏, and 𝑐 so that 𝑎1101+𝑏1001+𝑐0110=1013.

  • 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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