1:Find the determinant of the following mattrix [((2,-1,-6)),((-3,0,5)),((4,3,0))] 2: If told that matrix A is singular Matrix find the possible value(s) for x A = { (16x, 4x),(x,9):}

Question
Matrix transformations
asked 2021-02-06
1:Find the determinant of the following mattrix \([((2,-1,-6)),((-3,0,5)),((4,3,0))]\) 2: If told that matrix A is singular Matrix find the possible value(s) for x \(A = { (16x, 4x),(x,9):}\)

Answers (1)

2021-02-07
Given:
\(A=[[2,-1,-6],[-3,0,5],[4,3,0]]\)
As discussed above determinant of \(A=2(0-3*5)-(-1)[-3*0-4*5]+(-6)[-3*3-4*0]\)
=2(-15)+1(0-20)-6(-9-0)
=-30-20+54=4
Hence, he determinant of the given matrix=4
\(c.A=[[16x,4x],[x,9]]\)
We know when the matrix is single determinant is zero
Calculating the determinant of A
|A|=16*9-x*4x
\(=144-4x^2\)
Now, put |A|=0
i.e,
\(144-4x^2=0\)
\(4x^2=144\)
\(x^2=(144/4)=36\)
\(x^2=36=>x=sqrt(36)\)
\(x=pm6\)
Hence, x=-6 or x=6
(-6,=6)
0

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