यदि `A=[(1,-3),(2,k)]` और `A^(2)-4A+10I=A` है तब k बराबर है

Options

A. 0
B. `-4`
C. 4
D. 1 या 4

Answer

C

Explanation

`A^(2)-4A+10I=A`
`implies[(1,-3),(2,k)][(1,-3),(2,k)]-4[(1,-3),(2,k)]+10[(1,0),(0,1)]=[(1,-3),(2,k)]`
`implies[(-5,-3-3k),(2+2k,-6+k^(2))]-[(4,-12),(8,4k)]+[(10,0),(0,10)]=[(1,-3),(2,k)]`
`implies[(1,9-3k),(-6+2k4,+k^(2)-4k)]=[(1,-3),(2,k)]`
`implies9-3k=-3,-6+2k=2" "......(i)` और `4+k^(2)-4k=k`
`impliesk^(2)-5k+4=0impliesk=4,1`
लेकिन k=1 समीकरण (i) को संतुष्ट नहीं करता है।