Free Printable Matrices2

1.

The rank of the above (n+1) $\times$ (n+1) matrix where ‘a’ is real number is

a)

1

b)

2

c)

n

d)

depends on a

2.

1. Under which one of the following condition does the system of the equations have a unique solution?

a)

$for\ all\ a\in R$

b)

a=8

c)

$for\ all\ a\in Z$

d)

$a\ne8$

3.

The system of equations,

4x₁+ x₂- 3x₃- x₄=0,

2x₁+ 3 x₂+ x₃- 5x₄=0,

x₁- 2x₂- 2x₃+ 3x₄=0 has

a)

no solution

b)

only one solution

c)

infinite number of solutions

d)

only two solutions

4.

If m is a 7 x 5 matrix of rank 3 and N is a 5 x 7 matrix of rank 5, then rank (mn) is

a)

5

b)

3

c)

2

d)

1

5.

Solution of the system defined by the set of equations

4y+ 3z = 8,

3x –z = 2 and

3x+ 2y = 5 is

a)

x=0, y=1, z=4/3

b)

x=0, y=1/2, z=2

c)

x=1, y=1/2, z=2

d)

does not exist

6.

Let D be a non-zero n x n real matrix with n≥2 which of the following implications is valid?

a)

det(D) = 0 $\Longrightarrow$ rank(D) = 0

b)

a) det(D) = 1 $\Longrightarrow$ rank(D) $\ne$ 1

c)

rank(D) =1 $\Longrightarrow$ det(D) $\ne$ 0

d)

rank(D) = n $\Longrightarrow$ det(D) $\ne$ 1

7.

If B is a non-singular matrix and A is a square matrix, then det(B^-1AB) is equal to

a)

det (BAB)

b)

det (A)

c)

det (B^-1)

d)

det (A^-1)

8.

If A be an n x n matrix of rank n-2; n>2 then the rank of adj A is

a)

n

b)

n-1

c)

2

d)

0

9.

The system of equations x+y+z=0, 3x+6y+z=0, αx+2y+z=0 has infinitely many solutions then α is equal to

a)

7

b)

7/5

c)

5/7

d)

5

10.

1. The values of λ for which the equations are consistent

a)

1,1,1

b)

2,2,2

c)

0,3,3

d)

1,2,4

Matrices2

Total questions: 10

Worksheet time: 11mins

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