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Find the inverse of the following matric...

Find the inverse of the following matrics.
`[[2,-2],[4,3]]`

Text Solution

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Write A =[[2,-2],[4,3]]
Then adj A=[[3,2],[-4,2]] and |A|=6+8=14
Hence `A^(-1)adj A=[[[3,2],[-4,2]]]/14=[[3/14,-2/14],[-4/14,-1/14]]`=[[3/14,1/7],[-2/7,1/7]]`
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A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
  1. Verify A (adj A)=(adj A)A=|A|I in the following matrices. [[2,3],[-4,-...

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  2. Verify A (adj A)=(adj A)A=|A|I in the following matrices. [[2,3],[-4,-...

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  3. Find the inverse of the following matrics. [[2,-2],[4,3]]

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  4. Find the inverse of the following matrics. [[-1,5],[-3,2]]

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  5. Find the inverse of the following A=[[1,2,3],[0,2,4],[0,0,5]]

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  6. Find the inverse of the following A=[[1,0,0],[3,3,0],[5,2,-1]]

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  7. Find the inverse of the following A=[[2,1,3],[4,-1,0],[-7,2,1]]

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  8. Find the inverse of the following A=[[1,-1,2],[0,2,-3],[3,-2,4]]

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  9. Let A =[[3,7],[2,5]] and B=[[6,8],[7,9]]Verify that (AB)^(-1)=B^(-1)A^...

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  10. If A =[[3,1],[-1,2]],show that A^2-5A + 7I=0 Hence, find A^(-1)

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  11. For the matrix A=[[3,2],[1,1]],find the numbers a and b such that A^2+...

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  12. For the matrix A=[[1,1,1],[1,2,-3],[2,-1,3]] show that A^3-6A^2+5A+11I...

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  13. Let A be a non-singular square matrix of order 3xx3.Then |adj A| is .....

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  14. If A is an invertible matrix of order 2, then det(A^(-1))=

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  15. Examine the consistency of the following system of equation x+2y=12 ...

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  16. Examine the consistency of the following system of equation 2x-y =5 ...

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  17. Examine the consistency of the following system of equation x+3y =5 ...

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  18. Examine the consistency of the following system of equation x+y+z=1 ...

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  19. Test the consistency 3x-y-2z=2,2y-z=-1,3x-5y=3

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  20. Examine the consistency of the following system of equation 5x-y+4z=5...

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