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Lesson: Inverse of a 2x2 Matrix

Sample Question Videos

Worksheet • 22 Questions • 8 Videos

Q1:

Find the inverse of the following matrix.

  • A
  • B
  • C
  • D
  • E

Q2:

Find the inverse of the following matrix.

  • A
  • B
  • C
  • D
  • E

Q3:

Is the following matrix invertible?

  • Ano
  • Byes

Q4:

Is the following matrix invertible?

  • Ano
  • Byes

Q5:

Find the set of real values of π‘Ž for which 𝐴 = ο€Ό π‘Ž 2 5 1 π‘Ž  has a multiplicative inverse.

  • A ℝ βˆ’ { 5 , βˆ’ 5 }
  • B ℝ βˆ’ { 2 5 , 1 }
  • C { 5 , βˆ’ 5 }
  • D ℝ βˆ’ { 5 }
  • E ℝ

Q6:

Given that find 𝐴 βˆ’ 1 .

  • A βŽ› ⎜ ⎜ ⎝ 1 π‘₯ 1 0 1 𝑦 ⎞ ⎟ ⎟ ⎠ 3 3
  • B βŽ› ⎜ ⎜ ⎝ 1 π‘₯ βˆ’ 1 0 1 𝑦 ⎞ ⎟ ⎟ ⎠ 3 3
  • C βŽ› ⎜ ⎜ ⎝ βˆ’ 1 π‘₯ 0 1 βˆ’ 1 𝑦 ⎞ ⎟ ⎟ ⎠ 3 3
  • D βŽ› ⎜ ⎜ ⎝ 1 π‘₯ 0 1 1 𝑦 ⎞ ⎟ ⎟ ⎠ 3 3

Q7:

Are the following matrices multiplicative inverses of each other?

  • Ayes
  • Bno

Q8:

Find the inverse of the following matrix.

  • A
  • B
  • C
  • D
  • E

Q9:

Find the multiplicative inverse of the matrix 𝐴 = ο€½ βˆ’ 4 βˆ’ 1 0 3 5  , if possible.

  • A βŽ› ⎜ ⎜ ⎝ 1 2 1 βˆ’ 3 1 0 βˆ’ 2 5 ⎞ ⎟ ⎟ ⎠
  • B ο€½ βˆ’ 4 1 0 βˆ’ 3 5 
  • C 𝐴 has no multiplicative inverse.
  • D ο€½ 5 βˆ’ 1 0 3 βˆ’ 4 
  • E ο€½ 5 1 0 βˆ’ 3 βˆ’ 4 

Q10:

Given that the following matrix is invertible, what must be true of ?

  • A
  • B
  • C
  • D
  • E

Q11:

Using the elementary row operation, find for the given matrix if possible.

  • A
  • B
  • C
  • D
  • E

Q12:

Find the multiplicative inverse of 𝐴 =  βˆ’ 4 8 βˆ’ 1 2 2 4  , if possible.

  • A 𝐴 has no multiplicative inverse.
  • B βˆ’ 1 1 9 2  2 4 1 2 βˆ’ 8 βˆ’ 4 
  • C  2 4 1 2 βˆ’ 8 βˆ’ 4 
  • D βˆ’ 1 1 9 2  2 4 βˆ’ 8 1 2 βˆ’ 4 

Q13:

Given find its multiplicative inverse if possible.

  • A βˆ’ 1 3 7 ο€Ό βˆ’ 4 7 3 4 
  • B ο€Ό βˆ’ 4 7 3 4 
  • C 𝐴 has no multiplicative inverse.
  • D βˆ’ 1 3 7 ο€Ό βˆ’ 4 3 7 4 

Q14:

Find the multiplicative inverse of ο€Ό 6 9 0 0 6 9  .

  • A βŽ› ⎜ ⎜ ⎝ 1 6 9 0 0 1 6 9 ⎞ ⎟ ⎟ ⎠
  • B ο€Ό βˆ’ 6 9 0 0 βˆ’ 6 9 
  • C ο€Ό 6 9 0 0 βˆ’ 6 9 
  • D βŽ› ⎜ ⎜ ⎝ βˆ’ 1 6 9 0 0 βˆ’ 1 6 9 ⎞ ⎟ ⎟ ⎠

Q15:

Given that find the matrix 𝐴 .

  • A βŽ› ⎜ ⎜ ⎝ 1 βˆ’ 1 2 βˆ’ 3 5 1 5 ⎞ ⎟ ⎟ ⎠
  • B βŽ› ⎜ ⎜ ⎝ 1 5 1 2 3 5 1 ⎞ ⎟ ⎟ ⎠
  • C ο€Ό βˆ’ 1 0 βˆ’ 5 βˆ’ 6 βˆ’ 2 
  • D ο€Ό βˆ’ 1 0 5 6 βˆ’ 2 

Q16:

Consider the matrices 𝐴 and 𝐡 . Determine ( 𝐴 + 𝐡 )   𝐴 =  βˆ’ 3 βˆ’ 2 βˆ’ 5 βˆ’ 7  , 𝐡 =  βˆ’ 1 2 8 9  .

  • A  βˆ’ 0 . 2 5 0 0 . 3 7 5 0 . 5 
  • B  βˆ’ 4 0 3 2 
  • C  3 0 βˆ’ 4 2 
  • D  0 . 5 0 0 . 3 7 5 βˆ’ 0 . 2 5 

Q17:

Find the multiplicative inverse of

  • A ο€½ πœƒ βˆ’ πœƒ βˆ’ 1 πœƒ  s e c t a n s e c 2
  • B ο€½ πœƒ πœƒ 1 πœƒ  s e c t a n s e c 2
  • C ο€½ πœƒ βˆ’ 1 βˆ’ πœƒ πœƒ  s e c t a n s e c 2
  • D ο€½ πœƒ πœƒ πœƒ βˆ’ 1  t a n s e c s e c 2

Q18:

Find the multiplicative inverse of

  • A ο€Ό πœƒ πœƒ βˆ’ πœƒ πœƒ  s i n c o s c o s s i n
  • B ο€Ό πœƒ βˆ’ πœƒ πœƒ πœƒ  c o s s i n s i n c o s
  • C ο€Ό βˆ’ πœƒ πœƒ βˆ’ πœƒ βˆ’ πœƒ  c o s s i n s i n c o s
  • D ο€Ό πœƒ βˆ’ πœƒ πœƒ πœƒ  s i n c o s c o s s i n

Q19:

Solve for matrix in the matrix equation , where , , and are as follows.

  • A
  • B
  • C
  • D
  • E

Q20:

Consider the following matrix equation. Solve for the unknown matrix.

  • A
  • B
  • C
  • D
  • E

Q21:

Find the multiplicative inverse of the matrix 𝐴 = ο€½ 3 7 2 2  , if possible.

  • A βŽ› ⎜ ⎜ ⎝ βˆ’ 1 4 7 8 1 4 βˆ’ 3 8 ⎞ ⎟ ⎟ ⎠
  • B ο€½ 3 βˆ’ 7 βˆ’ 2 2 
  • C 𝐴 has no multiplicative inverse.
  • D ο€½ 2 7 2 3 
  • E ο€½ 2 βˆ’ 7 βˆ’ 2 3 

Q22:

Find the multiplicative inverse of the matrix 𝐴 = ο€½ 5 βˆ’ 2 7 βˆ’ 2  , if possible.

  • A βŽ› ⎜ ⎜ ⎝ βˆ’ 1 2 1 2 βˆ’ 7 4 5 4 ⎞ ⎟ ⎟ ⎠
  • B ο€½ 5 2 βˆ’ 7 βˆ’ 2 
  • C 𝐴 has no multiplicative inverse.
  • D ο€½ βˆ’ 2 βˆ’ 2 7 5 
  • E ο€½ βˆ’ 2 2 βˆ’ 7 5 
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