Home
Class 12
MATHS
Expess the matrix A=[{:(2,0,-4),(-3,1,5...

Expess the matrix `A=[{:(2,0,-4),(-3,1,5),(4,-2,3):}]` as a sum of symmetic and skew symmetric matrices.

Text Solution

Verified by Experts

The correct Answer is:
N/a
`A=[{:(2,0,-4),(-3,1,5),(4,-2,3):}]`
`implies A'=[{:(2,0,-4),(-3,1,5),(4,-2,3):}][{:(2,-3,4),(0,1,-2),(-4,5,3):}]`
`A+A'=[{:(2,0,-4),(-3,1,5),(4,-2,3):}]+[{:(2,-3,4),(0,1,-2),(-4,5,3):}]`
`=[{:(4,-3,0),(-3,2,3),(0,3,6):}]`
`implies (1)/(2)(A+A')=[{:(2,-3//2,0),(-3//2,1,3//2),(0,3//2,3):}]`
`and A-A'=[{:(2,0,-4),(-3,1,5),(4,-2,3):}]-[{:(2,-3,4),(0,1,-2),(-4,5,3):}]`
`=[{:(0,3,-8),(-3,0,7),(8,-7,0):}]`
`implies (1)/(2)(A-A')=[{:(0,3//2,-4),(-3//2,0,7//2),(4,-7//2,0):}]`
`Now A=(1)/(2)(A-A')+(1)/(2)(A-A')`
`implies [{:(2,0,-4),(-3,1,5),(4,-2,3):}]`
`=[{:(2,-3//2,0),(-3//2,1,3//2),(0,3//2,3):}]+[{:(0,3//2,-4),(-3//2,0,7//2),(4,-7//2,0):}].`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    NAGEEN PRAKASHAN|Exercise Exercise 3a|20 Videos

  • MATRICES

    NAGEEN PRAKASHAN|Exercise Exercise 3b|12 Videos

  • LINEAR PROGRAMMING

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|9 Videos

  • PROBABIILITY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Express the matrix A={:[(2,-3,4),(-1,4,3),(1,-2,3)]:} as the sum of a symmetric and a skew symmetric matrix

Express the matrix [(2,4,-6),(7,3,5),(1,-2,4)] as a sum of symmetric and a skew - symmetric matrix.

Express the matrix B= [{:(,2,-2,),(,-1,3,):}] as the sum of a symmetric and a skew symmetric matrix.

Express the matrix A=[{:(-1,5,1),(2,3,4),(7,0,9):}] as the sum of a symmetric and a skew-symmetric matrix.

Express the matrix B=[2,-2,-4-1,3,41,-2,-3] as the sum of a symmetric and a skew symmetric matrix.

Express the matrix A=[{:(2,3),(-1,4):}] as the sum of a symmetric matrix and a skew-symmetric matrix.

Express the matrix A=[{:(3,-4),(1,-1):}] as the sum of a symmetric matrix and a skew-symmetric matrix.

Express A=[(1,-1,2),(2,1,3),(4,-1,5)] as a sum of a symmetric and a skew symmetric matrix

Express [(3,-4),(1,-1)] as the sum of symmetric and skew-symmetric matrices.

Express the matrix A=[[3,2,3],[4,5,3],[2,4,5]] as the sum of symmetric and a skew symmetric matrix.