If A and B are square matrices of size n × n such that A 2 – B 2 = (A – B)(A + B), then which of the following will be always correct ?

either A or B is an identity matrix

JEE Questions for Maths Matrices And Determinants Quiz 2

Let M and N are two 3 × 3 non - singular skew-symmetric matrices such that MN = NM. If P^T denotes the transpose of P, then M²N² (M^T N)^-1 (MN^-1)^T is equal to

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M2
0%
- N2
0%
- M2
0%
MN

If χ is any matrix of order n × p (n and p are integers) and I is an identity matrix of order n × n, then the matrix M = I - χ (χ^' χ)^-1 χ^' is
I. idempotent matrix. II. Mχ = 0

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I is correct
0%
II is correct
0%
I is incorrect
0%
II is incorrect

If A_3×3 and |A|= 6, then |2adj A| is equal to

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48
0%
8
0%
288
0%
12

If A is 2 × 2 matrix and |A| = 2, then the matrix represented by |A (adj A)| is equal to

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0%
2)
0%
0%

If A is non - singular matrix of order 3, then adj (adj A) is equal to

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A
0%
A-1
0%
(1/|A|) A
0%
|A| A

Which one of the following is correct always for any two non - singular matrices A and B of same order ?

0%
AB = BA
0%
(AB)' = A' B'
0%
(A + B) (A - B) = A2 - B2
0%
(AB)-1 = B-1 A-1

Maths-Matrices and Determinants-38320.png

0%
2
0%
3
0%
- 4
0%
4
0%
- 2

Maths-Matrices and Determinants-38322.png

0%
2
0%
3
0%
0
0%
1

Maths-Matrices and Determinants-38324.png

0%
0%
2)
0%
0%

Maths-Matrices and Determinants-38330.png

0%
2A
0%
A
0%
- A
0%
I

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

0%
|A|n
0%
|A|n+1
0%
|A|n-1
0%
|A|n+2

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

0%
A
0%
A-1
0%
- A
0%
– A-1

Maths-Matrices and Determinants-38334.png

0%
0%
2)
0%
0%

If the system of equations χ + ky - z = 0, 3χ - ky - z = 0 and χ - 3y + z = 0, has non - zero solution, then k is equal to

0%
- 1
0%
0
0%
1
0%
2

The system of linear equation 3χ + y - z = 2, χ - z = 1 and 2χ + 2y + az = 5 has unique solution, when

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a ≠ 3
0%
a ≠ 4
0%
a ≠ 5
0%
a ≠ 2
0%
a ≠ 1

Maths-Matrices and Determinants-38342.png

0%
- 5
0%
5
0%
4
0%
1

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

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a + b - c = 0
0%
a - b + c = 0
0%
a + b + c ≠ 0
0%
a + b + c = 0

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

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p = 2
0%
p = - 2
0%
p = - (1/2)
0%
p = 3

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
Maths-Matrices and Determinants-38346.png

0%
0
0%
1
0%
2
0%
3

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

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rank (BA) = rank (A)
0%
rank (BA) ≥ rank (B)
0%
rank (BA) > rank (A)
0%
rank (BA) > rank (B)

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

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2
0%
- 2
0%
3
0%
- 3

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

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λ = 5
0%
λ = -5
0%
λ ≠ ± 5
0%
None of these

Let a, b and c be any real numbers. If there are real numbers χ, y and z not all zero such that χ = cy + bz, y = az + cχ and z = bχ + ay have non - zero solution. Then, a² + b² + c² + 2abc is equal to

0%
1
0%
2
0%
- 1
0%
0

The system of equations χ + y + z = 0, 2χ + 3y + z = 0 and χ + 2y = 0 has

0%
a unique solution; χ = 0, y = 0 and z = 0
0%
infinite solutions
0%
no solution
0%
finite number of non - zero solutions

Maths-Matrices and Determinants-38353.png

0%
(1 , 1 , 1)
0%
(0 , -1 , 2)
0%
(-1 , 2 , 2)
0%
(-1, 0 , 2)

The systems of equations χ + y + z = 8, χ - y + 2z = 6 and 3χ + 5y - 7z = 14 has

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no solution
0%
unique solution
0%
infinitely solutions
0%
None of the above

If a, b and c are positive real numbers. The following system of equations
Maths-Matrices and Determinants-38356.png

0%
infinite solutions
0%
unique solutions
0%
no solution
0%
finite number of solution

The simultaneous equations kχ + 2y - z = 1, (k - 1)y - 2z and (k + 2)z = 3 have only one solution, when

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k = -2
0%
k = -1
0%
k = 0
0%
k = 1

Maths-Matrices and Determinants-38359.png

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- 1
0%
2
0%
- 6
0%
4

The number of non - trivial solutions of the system χ - y + z = 0, χ + 2y - z = 0 and 2χ + y + 3z = 0, is

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0
0%
1
0%
2
0%
3

The system of equations 2χ + y - 5 = 0, χ - 2y + 1 = 0 and 2χ - 14y - a = 0 is consistent. Then, a is equal to

0%
1
0%
2
0%
5
0%
None of these

The values of λ and μ for which the system of equations χ + y + z = 6, χ + 2y + 3z = 10 and χ + 2y + λz = μ have infinite number of solutions, are

0%
λ = 3, μ = 10
0%
λ = 3, μ = ≠ 10
0%
λ ≠ 3, μ = 10
0%
λ ≠ 3, μ = ≠ 10

The system of equations 3χ - y + 4z = 3, χ + 2y - 3z = -2, 6χ + 5y + λz = -3 and has atleast one solutions, if

0%
λ = -5
0%
λ = 5
0%
λ = 3
0%
λ = -13

The values of a for which the system of equations χ + y + z = 0, χ + ay + az = 0 and χ - ay + z = 0 possesses non - zero solutions, are given by

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1 , 2
0%
1 , - 1
0%
1 , 0
0%
None of these

If the homogeneous system of linear equations pχ + y + z = 0, χ + qy + z = 0 and χ + y + rz = 0, where p, q, r ≠ 1, have a non - zero solution, then the value of
Maths-Matrices and Determinants-38366.png

Maths-Matrices and Determinants-38366.png

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- 1
0%
0
0%
2
0%
1

Maths-Matrices and Determinants-38368.png

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4
0%
3
0%
2
0%
1

If a system of the equations (α + 1)³χ + (α + 2)³y - (α + 3)³ = 0, (α + 1)χ + (α + 2)y - (α += 0 and χ + y - 1 = 0 is consistent. Then, what is the value of α ?

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1
0%
0
0%
- 3
0%
- 2

If X and Y are 2 x 2 matrices such that 2Y + 3Y = 0 and X + 2Y = I, where O and I denote the 2 x 2 zero matrix and the 2 x 2 identity matrix, then X is equal to

0%
0%
2)
0%
0%

The symmetric part of the matrix
Maths-Matrices and Determinants-38376.png

0%
0%
2)
0%
0%

Maths-Matrices and Determinants-38382.png

0%
0%
2)
0%
0%

If A and B are two symmetric matrices of order 3.
Statement I A(BA) and (AB) A are symmetric matrices.
Statement II AB is symmetric matrix, If matrix multiplication of A and B is commutative.

0%
Statement I is correct, Statement II is correct; Statement II is not a correct explanation for statement I
0%
Statement I is correct, Statement II is incorrect
0%
Statement I is incorrect, Statement II is correct
0%
Statement I is correct, Statement II is correct, Statement II is correct explanation for Statement I