Worksheet: Scalar Multiplication of Matrices

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In this worksheet, we will practice carrying out scalar multiplication of matrices.

Q1:

Given the matrix what is ?

  • A
  • B
  • C
  • D
  • E

Q2:

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

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

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 𝑥 .

Q6:

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

  • A − 2 𝐴 𝑍
  • B 2 𝑍 𝐴
  • C − 3 𝑍
  • D 5 𝐴
  • E 2 𝐴

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 × 𝑛 matrix 𝐴 are an orthonormal basis for ℂ 𝑛 , if and only if 𝐴 is a matrix.

  • Asymmetric
  • Bnormal
  • Csquare
  • Dunitary

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