# Cramer's Rule

## Trending Questions

**Q.**Using Cramer's rule or otherwise, the solution of equations:

x + y + z = 6

x - y + z = 2 and

3x + 2y - 4z = -5

is

- x = 2, y = 1, z = 3
- x = 2, y = 3, z = 1
- x = 1, y = 3, z = 2
- x = 1, y = 2, z = 3

**Q.**

There are three values of t for which the following system of equations has non-trivial solutions.

(a-t) x+by + cz=0

bx + (c - t) y +az=0

cx + ay + (b-t) z=0

We can express the product of the three values of t in the form of determainant as

D

**Q.**

If D≠0 and at least one of D1, D2, D3 is not 0 then according to Cramer's rule the system of linear equations will have

non trivial solution

trivial solution

infinite solutions

no solutions

**Q.**

Let a, b, c, be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x= cy +bz, y=az + cx and z = bx +ay. Then , a^{2} + b^{2}+ c^{2}+ 2abc is equal to

2

-1

0

1

**Q.**The system of equations

px+y+z=px+py+z=px+y+pz=p

has no solution for

- three distinct values of p
- two distinct values of p
- only one value of p
- no such p exists

**Q.**The system of equations x + y + z =2, 3x − y + 2z =6 and 3x + y + z =−18 has

- A unique solution
- No solutions
- An infinite number of solutions
- Zero solution as the only solution

**Q.**If the system of linear equation x+2ay+az = 0, x+3by+bz = 0, x+4cy+cz = 0 has a non zero solution, then a, b, c

- Are in A.P.
- Are in G. P.
- Are in H. P.
- Satisfy a +2b + 3c = 0

**Q.**If the system of linear equations

x+y+z=5

x+2y+3z=9

x+3y+αz=β

has infinitely many solutions, then β−α equals:

- 5
- 18
- 8
- 21

**Q.**

If D≠0 and at least one of D1, D2, D3 is not 0 then according to Cramer's rule the system of linear equations will have

non trivial solution

trivial solution

infinite solutions

no solutions

**Q.**

Total number of solutions to the system of linear equations 2x + 3y + z = 1, 4X + 6y + 2z = 3, 6x + 9y + 3z = 2 is

**Q.**

If D=0 and at least one of D1, D2, D3 is not 0 then according to Cramer's rule the system of linear equations will have

non trivial solution

trivial solution

infinite solutions

no solutions

**Q.**If the system of linear equations

x+y+z=5

x+2y+3z=9

x+3y+αz=β

has infinitely many solutions, then β−α equals:

- 5
- 18
- 8
- 21

**Q.**If a, b, c are non – zero real numbers and if the equations (a-1) x = y + z, (b -1)y = z + x, (c - 1)z = x + y has a non trivial solution, then ab + bc + ca is equal to

- a +b + c
- abc
- 1
- None of these

**Q.**

Which of the following cases will not lead to non trivial solutions in case of system of linear equations according to Cramer's rule Convention given D != 0 ?

D1 = 0, D2 = 0, D3 = 0

D1 = 0, D2 = 0, D3 != 0

D1 != 0, D2 != 0, D3 = 0

D1 != 0, D2 != 0, D3 != 0

**Q.**x + ky − z = 0, 3x − ky −z = 0 and x − 3y + z = 0 has non-zero solution for k =

- -1
- \N
- 1
- 2

**Q.**For which of the following ordered pairs (μ, δ), the system of linear equations

x+2y+3z=1

3x+4y+5z=μ

4x+4y+4z=δ

is inconsistent?

- (4, 6)
- (3, 4)
- (1, 0)
- (4, 3)

**Q.**

If D=0 and at least one of D1, D2, D3 is not 0 then according to Cramer's rule the system of linear equations will have

non trivial solution

trivial solution

infinite solutions

no solutions

**Q.**The value of k for which, the system of equations

kx + 3y - z = 1; x + 2y + z = 2 and -kx + y + 2z = -1 have no solution, is

- k = -7
- k = 7
- k=−72
- k=72

**Q.**

The system of linear equations x+y=0, x–y=0, z=0 will have

non trivial solution

trivial solution

infinite solutions

no solutions

**Q.**

Total number of solutions to the system of linear equations 2x + 3y + z = 1, 4X + 6y + 2z = 3, 6x + 9y + 3z = 2 is 1

True

False

**Q.**

Total number of solutions to the system of linear equations x + y + 0.z = 0, X – y + 0.z = 0, X + 4y + 0.z = 0 is infinity.

True

False

**Q.**The number of values of k for which the system of equations (k+1)x + 8y = 4k, kx + (k+3)y = 3k−1 has infinitely many solutions, is

- \N
- 1
- 2
- Infinite