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Worksheet: Invertible and Singular Matrices

Q1:

Is there any value of 𝑑 for which the matrix  1 0 0 0 𝑑 βˆ’ 𝑑 0 𝑑 𝑑 ο₯ c o s s i n s i n c o s has no inverse?

  • Ayes, when 𝑑 = πœ‹
  • Byes, when 𝑑 = πœ‹ 2
  • Cyes, when 𝑑 = πœ‹ 6
  • Dno
  • Eyes, when 𝑑 = πœ‹ 3

Q2:

Is there any value of 𝑑 for which the matrix has no inverse?

  • Ayes, when 𝑑 = 1
  • Byes, when 𝑑 = 0
  • Cno
  • Dyes, the matrix has no inverse for all values of 𝑑
  • Eyes, when 𝑑 = πœ‹

Q3:

Under what condition on π‘˜ is the matrix  βˆ’ 6 βˆ’ π‘˜ βˆ’ 6 1 2 1 1 βˆ’ π‘˜  invertible?

  • A π‘˜ is any real number.
  • B π‘˜ = 2 or π‘˜ = 3
  • C π‘˜ β‰  βˆ’ 6 and π‘˜ β‰  1 1
  • D π‘˜ β‰  2 and π‘˜ β‰  3
  • E π‘˜ = 2 or π‘˜ = βˆ’ 3

Q4:

Find the set of real values of for which has a multiplicative inverse, where .

  • A
  • B
  • C
  • D

Q5:

Find the value of that makes the matrix singular.

  • A
  • B40
  • C
  • D

Q6:

Find the set of real values of for which has a multiplicative inverse.

  • A
  • B
  • C
  • D
  • E

Q7:

Is there any value of 𝑑 for which the matrix has no inverse?

  • A yes, when 𝑑 = 1
  • B yes, when 𝑑 = 0
  • C yes, when 𝑑 = βˆ’ 1
  • D no
  • E yes, when 𝑑 = 2

Q8:

Find the value of that makes the following matrix singular.

Q9:

For the matrix does there exist a value of 𝑑 for which it fails to have an inverse? if so, what is this value?

  • A yes, when 𝑑 = βˆ’ 1 .
  • B yes, when 𝑑 = βˆ’ ο„ž 2 3 3 .
  • C yes, when 𝑑 = βˆ’ 2 .
  • D yes, when 𝑑 = βˆ’ √ 2 3 .
  • E yes, when 𝑑 = βˆ’ 2 3 .

Q10:

Under what condition on π‘Ž and 𝑏 is the matrix  π‘Ž 2 𝑏 5  invertible?

  • A 2 π‘Ž + 5 𝑏 β‰  0
  • B 2 𝑏 = 5 π‘Ž
  • C 5 𝑏 β‰  2 π‘Ž
  • D 2 𝑏 β‰  5 π‘Ž
  • E π‘Ž β‰  𝑏

Q11:

Find the set of real values of for which has no multiplicative inverse.

  • A
  • B
  • C
  • D
  • E

Q12:

Find the set of real values of that make the following matrix singular.

  • A
  • B
  • C
  • D

Q13:

Is the matrix  3 1 βˆ’ 3 βˆ’ 1  invertible?

  • ANo
  • BYes

Q14:

Find the set of real values of π‘Ž for which  π‘Ž 8 8 π‘Ž  has no multiplicative inverse.

  • A { 8 }
  • B { βˆ’ 6 4 , 6 4 }
  • C { 6 4 }
  • D { βˆ’ 8 , 8 }

Q15:

Find the set of real values of for which the following matrix has a multiplicative inverse.

  • A
  • B
  • C
  • D
  • E

Q16:

Which of the following matrices is singular?

  • A
  • B
  • C
  • D

Q17:

Which of the following matrices is singular?

  • A
  • B
  • C
  • D

Q18:

Which of the following matrices is singular?

  • A
  • B
  • C
  • D

Q19:

Does the following matrix have a multiplicative inverse?

  • Ano
  • Byes

Q20:

Find the set of real values of that make the following matrix singular.

  • A
  • B
  • C
  • D

Q21:

Find all the values of , where , which make the following matrix singular.

  • A ,
  • B ,
  • C ,
  • D ,

Q22:

Find all the values of for which the matrix is singular.

  • A4
  • B
  • C196
  • D