# 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
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 $$A = { (16x, 4x),(x,9):}$$

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)

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