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CBSE Class 12-science Answered

Find  adj.
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Asked by alanpeter9611 | 17 Feb, 2019, 02:44: AM
answered-by-expert Expert Answer
Given matrix A = begin mathsize 12px style open square brackets table row cell cos alpha end cell cell negative sin alpha end cell 0 row cell sin alpha end cell cell cos alpha end cell 0 row 0 0 1 end table close square brackets end style
|A| = cos2α + sin2α = 1
 
Let Cij be the cofactor of i-th row and j-th column
 
C11 = cosα ,  C12 = - sinα ,  C13 = 0
C21 = sinα ,  C22 = cosα ,  C23 = 0
C31 = 0 ,      C32 = 0 ,       C33 = 1
 
adj.A = begin mathsize 12px style open square brackets table row cell cos alpha end cell cell sin alpha end cell 0 row cell negative sin alpha end cell cell cos alpha end cell 0 row 0 0 1 end table close square brackets end style
 
A(adj.A) = begin mathsize 12px style open square brackets table row cell cos alpha end cell cell negative sin alpha end cell 0 row cell sin alpha end cell cell cos alpha end cell 0 row 0 0 1 end table close square brackets end stylebegin mathsize 12px style open square brackets table row cell cos alpha end cell cell sin alpha end cell 0 row cell negative sin alpha end cell cell cos alpha end cell 0 row 0 0 1 end table close square brackets end style = begin mathsize 12px style open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets end style
similarly we can prove the product of (adj.A)A is unit matrix
Since |A| = 1, it is proved for the given matrix,  A(adj.A) = (adj.A)A = |A|I3 , where I3 is unit matrix of order 3×3
Answered by Thiyagarajan K | 18 Feb, 2019, 12:08: AM

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