Matrices and Determinants Test

Result

Matrices and Determinants Test - 9

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
4 / -1

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

A
1

B
2

C
- 1

D
0

Solution
Question 2
4 / -1

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

A
a unique solution; χ = 0, y = 0 and z = 0

B
infinite solutions

C
no solution

D
finite number of non - zero solutions

Solution
Question 3
4 / -1

A
(1 , 1 , 1)

B
(0 , -1 , 2)

C
(-1 , 2 , 2)

D
(-1, 0 , 2)

Solution
Question 4
4 / -1

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

A
no solution

B
unique solution

C
infinitely solutions

D
None of the above

Solution
Question 5
4 / -1

If a, b and c are positive real numbers. The following system of equations

A
infinite solutions

B
unique solutions

C
no solution

D
finite number of solution

Solution
Question 6
4 / -1

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

A
k = -2

B
k = -1

C
k = 0

D
k = 1

Solution
Question 7
4 / -1

A
- 1

B
2

C
- 6

D
4

Solution
Question 8
4 / -1

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

A
0

B
1

C
2

D
3

Solution
Question 9
4 / -1

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

A
1

B
2

C
5

D
None of these

Solution
Question 10
4 / -1

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

A
λ = 3, μ = 10

B
λ = 3, μ = ≠ 10

C
λ ≠ 3, μ = 10

D
λ ≠ 3, μ = ≠ 10

Solution