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Lesson: Scalar Multiplication of Matrices

In this lesson, we will learn how to carry out scalar multiplication of matrices.

Worksheet • 8 Questions

Q1:

Given the matrix what is ?

  • A
  • B
  • C
  • D
  • E

Q2:

Given that ⃑ 𝐴 = ( βˆ’ 1 , βˆ’ 8 ) , find 3 ⃑ 𝐴 .

  • A ( βˆ’ 3 , βˆ’ 2 4 )
  • B ( βˆ’ 2 4 , βˆ’ 3 )
  • C ( βˆ’ 1 , βˆ’ 2 4 )
  • D ( βˆ’ 3 , βˆ’ 8 )

Q3:

Using the properties of determinants, find the value of

Q4:

Find numbers , , and so that .

  • A , ,
  • B , ,
  • C , ,
  • D , ,
  • E , ,

Q5:

Given that find the value of π‘₯ .

Q6:

Let 𝑍 be a 2 Γ— 3 matrix whose entries are all zero. If 𝐴 is any 2 Γ— 3 matrix, which of following is equivalent to 5 𝐴 βˆ’ 3 𝑍 ?

  • A 5 𝐴
  • B 2 𝐴
  • C 2 𝑍 𝐴
  • D βˆ’ 3 𝑍
  • E βˆ’ 2 𝐴 𝑍

Q7:

Let and be the identity matrix. Find , , and their product , and then use this to express as a combination of and .

  • A , , , .
  • B , , , .
  • C , , , .
  • D , , , .
  • E , , , .

Q8:

Fill in the blank. Columns of an 𝑛 Γ— 𝑛 matrix 𝐴 are an orthonormal basis for β„‚ 𝑛 , if and only if 𝐴 is a matrix.

  • Aunitary
  • Bnormal
  • Csquare
  • Dsymmetric
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