Question # 1

A = [3] is a/an

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Square matrix

Scalar matrix

Diagonal matrix

Identity matrix

For non-trival solution |A| is

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non zero

A = 0

|A| = 0

At = 0

A square matrix all of whose elements except the main diagonal are zeros is called a

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Null matrix

Singular matrix

Symmetric matrix

Diagonal matrix

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a²b²c²

4a²b²c²

4abc

None

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4A - 3I

3A - 4I

A - I

None of these

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3 x 1

1 x 3

3 x 3

1 x 1

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0

Independent of a

Independent of b

Independent of c

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I

14 I

0

None of these

If A and B are two matrices such that AB = B and BA =A, then A²+ B²=

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2 AB

2 BA

A + B

AB

For a square matrix A, if A = A^t, then A is called

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matrix

Transpose

Symmetric

Non-symmetric

The square matrix A is skew-symmetric when At =

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-B

-C

-A

-D

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A

-A

A^t

A^-

If the trace of matrix A is 5, then the trace of the matrix 3A is

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3/5

5/3

8

15

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Null matrix

Triangular matrix

Unit matrix

Rectangular matrix

The transpose of a column matrix is a ______

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Zero matrix

Diagonal matrix

Column matrix

Row matrix

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If A = [a_ij] is (m x n) matrix, then transpose of A is of the order

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m x m

m x n

n x n

n x m

If there are m rows and n columns in a matrix then its order is

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m x n

m x m

n x n

n x m

Every identity matrix is

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Row-vector

Scalar

Column-vector

All

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5

15

10

20

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16

None of these

Trival solution of homogeneous linear equation is

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(0, 0, 0)

(1, 2, 3)

(1, 3, 5)

a.b and c

If A and B are two matrices such that AB = B and BA = A then A2 + B2 =

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2 AB

2 BA

A + B

AB

Trival solution of homogeneous linear equation is

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(0, 0, 0)

(1, 2, 3)

(1, 3, 5)

a, b and c

The matrix A is Hermitian when (A)' =

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A

-A

A

A'

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x =0, y =4

x = -1, y = 2

x = 2, y = 3

x = 3, y = 4

Two matrices A and B are conformable for the product AB if

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Both A and B are square

Both A and B are symmetric

Number of rows of A = number of columns of B

Number of columns of A = number of rows of B

A square matrix A = [aij] is upper triangular when

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cij = 0

bij = 0

aij = 0 for all i > j

dij = 0

Let A be a square matrix. Then, 1/2 (A-A') is

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Skew-symmetric

Symmetric

Null

None of the above

If A and B are skew-symmetric then (AB)t is

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At Bt

AB

-AB

BA

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A²- 5A + 7I = 1

2A²- 3A + 7I = 0

A²- 5A + I = 0

A²- 5A + 7I = 0

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