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If the matrix {:[(a+b,0,0),(0,b+c,0),(0...

If the matrix `{:[(a+b,0,0),(0,b+c,0),(0,0,c+a)]:}`, (where a,b,c are positive integers) is a scalar matrix, then the value of (a+b+c) can be

A

6

B

8

C

5

D

7

Text Solution

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The correct Answer is:
A
In a scalar matrix, principal diagonal elements are same.
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PEARSON IIT JEE FOUNDATION-MATRICES-CONCEPT APPLICATION LEVEL 1
  1. If A={:[(4,-2),(3,-1),(2,5)]:}andB={:[(-7,2),(5,9),(3,4)]:}, then 2A+7...

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  2. If A={:((1,-3,4),(2,1,-2)):},B={:((-2,-4,5),(1,-1,3)):} and 5A-3B+2X=O...

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  3. If the matrix {:[(a+b,0,0),(0,b+c,0),(0,0,c+a)]:}, (where a,b,c are p...

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  4. If A{:[(1,4,-3),(5,7,9)]:}andB={:[(5,-7),(4,5)]:}, then

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  5. If {:[(0,3,-5),(-3,0,6),(5,-6,0)]:} is a

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  6. If A={:[(2,4),(-3,7)]:}andB=A^(T)," then "A^(T)+B^(T) is

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  7. If A and B are commute then (A+B)^(2) =

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  8. If A={:[(2,-3,1)]:}andB={:[(4),(2),(-2)]:}, then find 2A^(T)+B

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  9. If {:[(p),(q),(r)]:}andB={:[(3,4,5)]:}, then AB is

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  10. If the orders of matrices A^(T),BandC^(T)" are "3xx4,2xx3and1xx2 respe...

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  11. A is a 2xx2 matrix, such that A={:[(a(ij))]:}, where a(ij)=2i-j+1. The...

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  12. If A+B={:[(01,-11),(9,7)]:}andA-B={:[(-8,9),(9,-5)]:}, then B=

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  13. If A={:((-2,-1),(-5,-3)):}B={:((-3,1),(5,-2)):}and(AB)^(n)=I then n is...

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  14. If A={:((4,3),(-5,2)):}, then A^(2)-6A =

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  15. If A={:((1,5),(3,6)):}and=((34)/(39)), then find the matrix X such tha...

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  16. If {:((2,3),(p,1)):}{:((5,2),(-4,6)):}={:((-2,q),(16,r)):}, then 2p+r=

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  17. If A={:((2,-2),(-2,2)):},B={:((5,3),(-7,2)):}and=C={:((4,2),(-8,1)):} ...

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  18. A={:[(-5,-3,4),(3,2,-4)]:}andB={:[(-4,5,-2),(3,1,5)]:}, then find X s...

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  19. If A+B={:[(7,6),(-3,2)]:}andA-B={:[(1,2),(3,6)]:}, then find A.

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  20. If B-A^(T)={:[(3,4,-2),(5,-3,7)]:}andB^(T)+A={:[(2,0),(5,-1),(3,4)]:},...

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