Matrices and Determinants Test

Result

Matrices and Determinants Test - 8

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

A
2A

B
A

C
- A

D
I

Solution
Question 2
4 / -1

If A is an invertible matrix of order n, then the determinant of adj (A) is

A
|A|ⁿ

B
|A|ⁿ⁺¹

C
|A|^n-1

D
|A|ⁿ⁺²

Solution
Question 3
4 / -1

If A is a non – singular matrix that A³ = A + I, then the inverse of B = A⁶ - A⁵ is

A
A

B
A^-1

C
- A

D
– A^-1

Solution
Question 4
4 / -1

A

B

C

D

Solution
Question 5
4 / -1

The system of equations -2χ + y + z = a, χ - 2y + z = b and χ + y - 2z = c is constant, if

A
a + b - c = 0

B
a - b + c = 0

C
a + b + c ≠ 0

D
a + b + c = 0

Solution
Question 6
4 / -1

If the system of linear equations χ + 2y - 3z = 1, (p + 2)z = 3 and (2p + 1)y + z = 2has no solutions, then

A
p = 2

B
p = - 2

C
p = - (1/2)

D
p = 3

Solution
Question 7
4 / -1

If the system of equations aχ + ay - z = 0, bχ - y + bz = 0 and -χ + cy + cz = 0 has a non - trivial solution, then the value of

A
0

B
1

C
2

D
3

Solution
Question 8
4 / -1

If B is an invertible matrix and A is a matrix, then

A
rank (BA) = rank (A)

B
rank (BA) ≥ rank (B)

C
rank (BA) > rank (A)

D
rank (BA) > rank (B)

Solution
Question 9
4 / -1

The real value of k for which the system of equations 2kχ - 2y + 3z = 0, χ + ky + 2z = 0 and 2χ + kz = 0, has non - trivial solution is

A
2

B
- 2

C
3

D
- 3

Solution
Question 10
4 / -1

If the system of homogeneous equations 2χ - 2y + z = 0, χ - 2y + z = 0 and λχ - y + 2z = 0 has infinitely many solutions, then

A
λ = 5

B
λ = -5

C
λ ≠ ± 5

D
None of these

Solution