Test: Matrices- 2

Question 1

Accepted Answer

a nilpotent matrix

Answer

an invertible matrix

Answer

an idempotent matrix

Answer

none of these

Question 2

Accepted Answer

Answer

Answer

Answer

none of these.

Question 3

If A any square matrix then which of the following is not symmetric ?

Accepted Answer

A&#8722;At

Answer

A+At

Answer

AAt

Answer

AtA

Question 4

Let a, b, c, d, u, v be integers. If the system of equations, a x + b y = u, c x + dy = v, has a unique solution in integers, then

Accepted Answer

ad - bc need not be equal to ±1.

Answer

ad – bc = ±1

Answer

ad – bc = - 1

Answer

ad – bc = 1

Question 5

The system of equations, x + y + z = 1, 3 x + 6 y + z = 8, αx + 2 y + 3z = 1 has a unique solution for

Accepted Answer

all integral α

Answer

α not equal to 0

Answer

all rational α

Answer

all real α

Question 6

If A and B are symmetric matrices of the same order, then

Accepted Answer

AB + BA is a symmetric matrix

Answer

AB is symmetric matrix

Answer

AB – BA is a symmetric matrix

Answer

A – B is a skew-symmetric matrix

Question 7

If A = [a_ij]_2×2 where a_ij= i + j, then A is equal to

Accepted Answer

Answer

Answer

Answer

Question 8

Each diagonal element of a skew-symmetric matrix is

Accepted Answer

Zero

Answer

negative.

Answer

non-real

Answer

Positive

Question 9

The system of equations, x + y + z = 6, x + 2 y + 3 z = 14, x + 3 y + 5z = 20 has

Accepted Answer

no solution.

Answer

infinitely many solutions

Answer

a unique solution

Answer

only finitely many solutions

Question 10

The matrix of the transformation ‘reflection in the line x + y = 0 ‘ is

Accepted Answer

Answer

Answer

Answer

Question 11

A square matrix A = [a_ij]_n×n is called a diagonal matrix if a_ij = 0 for

Accepted Answer

I&#160;&#8800;&#160;j

Answer

I&#160;&#60;&#160;j

Answer

I&#160;=&#160;j

Answer

I&#160;&#62;&#160;j

Question 12

If and then AB =

Accepted Answer

0

Answer

B2

Answer

A3

Answer

1

Question 13

Accepted Answer

a symmetric matrix

Answer

a unit matrix

Answer

a skew- symmetric matrix.

Answer

a diagonal matrix

Question 14

If I_n is the identity matrix of order n, the (In)⁻¹

Accepted Answer

= In

Answer

= O

Answer

n = In

Answer

does not exist

Question 15

If A = [x y z], and C = [xyt]^t, then ABC is

Accepted Answer

1×1 matrix

Answer

3×3 matrix

Answer

not defined

Answer

none of these.

Question 16

If a square matrix A has two identical rows or columns , then det.A is :

Accepted Answer

0

Answer

-1

Answer

1

Answer

none of these.

Question 17

For a skew symmetric odd ordered matrix A of integers, which of the following will hold true:

Accepted Answer

det(A) = 0

Answer

det(A) = 9

Answer

det(A) = 81

Answer

et(A) = 4

Question 18

Matrix A when multiplied with Matrix C gives the Identity matrix I, what is C?

Accepted Answer

Inverse of A

Answer

Identity matrix

Answer

Square of A

Answer

Transpose of A

Question 19

Let for any matrix M ,M⁻¹exist. Which of the following is not true.

Accepted Answer

(M⁻¹)⁻¹ = (M⁻¹)¹

Answer

(M⁻¹)² = (M²)⁻¹

Answer

(M⁻¹)⁻¹ = (M)

Answer

none of these.

Question 20

Rank of a non-zero matrix is always

Accepted Answer

&#10878;1

Answer

0

Answer

greater than 1

Answer

equal to 1

Question 21

For a non-trivial solution | A | is

Accepted Answer

|A| = 0

Answer

|A| > 0

Answer

|A| < 0

Answer

|A| &ne; 0

Question 22

If for a matrix A, A²+I = O where I is the identity matrix, then A equals

Accepted Answer

Answer

Answer

Answer

Question 23

Accepted Answer

A = - A&rsquo;

Answer

A = A&rsquo;

Answer

A = - A

Answer

None of these.

Question 24

The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y - kz = 4 has a unique solution if ,

Accepted Answer

k &#8800; 0

Answer

k = 0

Answer

− 1 < k < 1

Answer

− 2 < k < 2

Question 25

The value of k for which the system of equations, x + k y + 3 z = 0, 3 x + k y – 2 z = 0, 2 x + 3 y – 4 z = 0, have a non-trival solution is

Accepted Answer

33/2

Answer

2/33

Answer

33

Answer

none of these

Matrices- 2 - Free MCQ Practice Test with solutions, JEE Maths

MCQ Practice Test & Solutions: Test: Matrices- 2 (25 Questions)

If A any square matrix then which of the following is not symmetric ?

Let a, b, c, d, u, v be integers. If the system of equations, a x + b y = u, c x + dy = v, has a unique solution in integers, then

The system of equations, x + y + z = 1, 3 x + 6 y + z = 8, αx + 2 y + 3z = 1 has a unique solution for

If A and B are symmetric matrices of the same order, then

If A = [a_ij]_2×2 where a_ij= i + j, then A is equal to

Each diagonal element of a skew-symmetric matrix is

The system of equations, x + y + z = 6, x + 2 y + 3 z = 14, x + 3 y + 5z = 20 has

The matrix of the transformation ‘reflection in the line x + y = 0 ‘ is

A square matrix A = [a_ij]_n×n is called a diagonal matrix if a_ij = 0 for

If and then AB =

If I_n is the identity matrix of order n, the (In)⁻¹

If A = [x y z], and C = [xyt]^t, then ABC is

If a square matrix A has two identical rows or columns , then det.A is :

For a skew symmetric odd ordered matrix A of integers, which of the following will hold true:

Matrix A when multiplied with Matrix C gives the Identity matrix I, what is C?

Let for any matrix M ,M⁻¹exist. Which of the following is not true.

Rank of a non-zero matrix is always

For a non-trivial solution | A | is

If for a matrix A, A²+I = O where I is the identity matrix, then A equals

The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y - kz = 4 has a unique solution if ,

The value of k for which the system of equations, x + k y + 3 z = 0, 3 x + k y – 2 z = 0, 2 x + 3 y – 4 z = 0, have a non-trival solution is

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Matrices- 2 - Free MCQ Practice Test with solutions, JEE Maths

MCQ Practice Test & Solutions: Test: Matrices- 2 (25 Questions)

If A any square matrix then which of the following is not symmetric ?

Let a, b, c, d, u, v be integers. If the system of equations, a x + b y = u, c x + dy = v, has a unique solution in integers, then

The system of equations, x + y + z = 1, 3 x + 6 y + z = 8, αx + 2 y + 3z = 1 has a unique solution for

If A and B are symmetric matrices of the same order, then

If A = [aij]2×2 where aij= i + j, then A is equal to

Each diagonal element of a skew-symmetric matrix is

The system of equations, x + y + z = 6, x + 2 y + 3 z = 14, x + 3 y + 5z = 20 has

The matrix of the transformation ‘reflection in the line x + y = 0 ‘ is

A square matrix A = [aij]n×n is called a diagonal matrix if aij = 0 for

If and then AB =

If In is the identity matrix of order n, the (In)−1

If A = [x y z], and C = [xyt]t, then ABC is

If a square matrix A has two identical rows or columns , then det.A is :

For a skew symmetric odd ordered matrix A of integers, which of the following will hold true:

Matrix A when multiplied with Matrix C gives the Identity matrix I, what is C?

Let for any matrix M ,M−1exist. Which of the following is not true.

Rank of a non-zero matrix is always

For a non-trivial solution | A | is

If for a matrix A, A2+I = O where I is the identity matrix, then A equals

The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y - kz = 4 has a unique solution if ,

The value of k for which the system of equations, x + k y + 3 z = 0, 3 x + k y – 2 z = 0, 2 x + 3 y – 4 z = 0, have a non-trival solution is

Mathematics (Maths) for JEE Main & Advanced

Mathematics (Maths) for JEE Main & Advanced

Top Courses for JEE

About this JEE Practice Test

Explore more JEE Study Resources

If A = [a_ij]_2×2 where a_ij= i + j, then A is equal to

A square matrix A = [a_ij]_n×n is called a diagonal matrix if a_ij = 0 for

If I_n is the identity matrix of order n, the (In)⁻¹

If A = [x y z], and C = [xyt]^t, then ABC is

Let for any matrix M ,M⁻¹exist. Which of the following is not true.

If for a matrix A, A²+I = O where I is the identity matrix, then A equals