1.

Find the inverse the matrix (if it exists)given in`[0 0 0 0cosalphasinalpha0sinalpha-cosalpha]`

Answer» `"Let A="|{:(1,0,0),(0,"cos"alpha,"sin"alpha),(0,"sin"alpha,"-cos"alpha):}|`
`rArr" |A| ="|{:(1,0,0),(0,"cos"alpha,"sin"alpha),(0,"sin"alpha,"-cos"alpha):}|`
`=1(cos^(2)alpha-sin^(2)alpha)-0=-1ne0`
`A_(11)=(-1)^(2)(-cos^(2)alpha-sin^(2)alpha)=-1`
`A_(12)=(-1)^(3) (0-0)=0`
`A_(13)=9-1)^(4)(0-0)=0`
`A_(21)=(-1)^(3)(0-0)=0`
`A_(22)=(-1)^(4)(-cos alpha - 0)=-cos alpha`
`A_(23)(-1)^(5)(sin alpha-0)=0`
`A_(31)=(-1)^(4)(0-0)=0`
`A_(32)=(-1)^(5)(sin alpha -0) = - sin alpha`,
`A_(33)=(-1)^(6)(cos alpha -0) = cos alpha`
`|{:(1,0,0),(0,"-cos"alpha,"-sin"alpha),(0,"-sin"alpha,"cos"alpha):}|=|{:(-1,0,0),(0,"-cos"alpha,"-sin"alpha),(0,"-sin"alpha,"cos"alpha):}|`
`"Now A"^(-1)=1/|A|"adj A"=1/-1|{:(-1,0,0),(0,"-cos"alpha,"-sin"alpha),(0,"-sin"alpha,"cos"alpha):}|`
`=|{:(1,0,0),(0,"cos"alpha,"sin"alpha),(0,"sin"alpha,"-cos"alpha):}|`


Discussion

No Comment Found

Related InterviewSolutions