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Let alpha, lambda , mu in R.Consider th...

Let `alpha, lambda , mu in R`.Consider the system of linear equations
`alphax+2y=lambda`
`3x-2y=mu`
Which of the following statement(s) is (are) correct ?

A

(a) If a = -3, then the system has infinitely many solutions for all value of `lambda and mu`.

B

If `a ne -3`, then the system has a unique solution fopor all values of `lambda and mu`.

C

If `lambda+u=0`, then the system has infinitely many solutions for a = -3`.

D

If `lambda +mu ne 0`, then the system has no solutions for a = -3.

Text Solution

Verified by Experts

The correct Answer is:
A
If a = -3, then the two equations in the given system represent parallel lines for `-lambda ne mu i.e., lambda+mu ne 0` and so the system has no solution. So, option (d) is correct.
If a = -3 and `lambda+mu=0 i.e., -lambda=mu`, then the two lines given by the above system are coincident and hence the system has infinitely many solutions. So, option (c) is correct for all values of `lambda and mu`.
If `a ne -3`, then the two lines given in the system are not parallel i.e.,they are intersecting and hence the ststem has a unique solutions. So, option (b) is correct.
Clearly, option(a) incorrect.
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OBJECTIVE RD SHARMA ENGLISH-MATRICES-Chapter Test
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  2. If A is an invertible matrix and B is a matrix, then

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  4. If {:A=[(a,0,0),(0,b,0),(0,0,c)]:}," then "A^(-1), is

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  5. The inverse of the matrix {:[(1,3),(3,10)]:} is equal to

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  6. If {:A=[(5,2),(3,1)]:}," then "A^(-1)=

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  7. If {:X=[(3,-4),(1,-1)]:}, the value of X^n is equal to

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  8. If {:A=[(5,2),(3,1)]:}," then "A^(-1)=

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  9. For the system of equations: x+2y+3z=1 2x+y+3z=2 5x+5y+9z=4

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  10. If {:A=[(3,1),(-1,2)]:}," then "A^(2)=

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  11. if A=[(4,x+2),(2x-3,x+1)] is symmetric, then x is equal to

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  12. If A+B={:[(1,0),(1,1)]:}andA-2B={:[(-1,1),(0,-1)]:}, then A is equal t...

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  13. {:[(-6,5),(-7,6)]^(-1)=:}

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  14. From the matrix equation AB=AC, we conclude B=C provided.

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  15. If I3 is the identily matrix of order 3, then (I3)^(-1)=

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  16. Let a ,b , c be real numbers. The following system of equations in x ,...

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  17. If A and B are two matrices such that A+B and AB are both defind, then

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  18. A and B are tow square matrices of same order and A' denotes the tran...

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  19. STATEMENT-1: The lines a(1)x+b(1)y+c(1)=0a(2)x+b(2)y+c(2)=0,a(3)x+b(3)...

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  20. The system of linear equations x+y+z=2,2x+y-z=3, 3x+2y+kz=4 has a uniq...

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  21. If A and B ar square matrices of order 3 such that |A|=-1|B|=3, then |...

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