Important Questions of Determinants Mathematics | Zigya

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 Multiple Choice QuestionsMultiple Choice Questions

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141.

Let A be a 3 × 3 matrix such thatadj A = 2 - 11 - 1021 - 2 - 1 and B = adjadj A

If A = λ and B - 1T = μ, Then the ordered pair, λ, μ is equal to

  • 3, 181

  • 9, 19

  • (3, 81)

  • 9, 181


142.

If the system of equations

x + y + z = 22x + 4y  z = 63x + 2y + λz = μ

  • λ + 2μ = 14

  • 2λ - μ = 5

  • 2λ + μ = 14

  • λ - 2μ = - 5


143.

Let λ  R. The system of linear equations2x1 - 4x2 + λx3 = 1x1 - 6x2 + x3  = 2λx1 - 10x2 + 4x3 = 3is inconsistant for : 

  • every value of λ

  • exactly two values of λ

  • exactly one positive value of λ

  • exactly one negative value of λ


144.

If the system of linear equations

x + y + 3z = 0

x + 3y + k2z = 0

3x + y + 3z = 0

has a non–zero solution (x, y, z) for some k  R, then x x + yz is equal to :

  •  - 9

  •  - 3

  • 9

  • 3


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145.

The values of λ and μ for which the system of linear equations 

x + y + z = 2

x + 2y + 3z = 5

x + 3y + λz = μ

has infinitely many solutions are respectively :

  • 5 and 8

  • 4 and 9

  • 6 and 8

  • 5 and 7


146.

Let θ = θ5 and A = cosθsinθ - sinθcosθ. If B = A + A4, Then detB : 

  • 0

  • 1

  • lies in (2, 3)

  • lies in (1, 2)


 Multiple Choice QuestionsShort Answer Type

147.

The sum of distinct values of l for which the system of equations:(λ  1)x + (3λ + 1)y + 2λz = 0(λ 1)x + (4λ  2)y + (λ + 3)z = 02x + (3λ + 1)y + 3(λ  1)z = 0,Has non-zero solutions, is...


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