Find 𝑘 such that the following matrix 𝑀 is singular.

Question

Find k such that the following matrix M is singular.

[4 2 4 ]

[-12 -7 -15 ] = M

[-44+k -20 -42 ]

k=

Answer 1

Matrix is singular if the determinant is 0

Find the det(M) and that will give you an expression involving k. Then set that expression equal to 0 in order to find the value of k.

det(M)= 4[(-7)(-42)-(-15)(-20)] - 2[(-12)(-42)-(-15)(-44+k)] +4[(-12)(-20)-(-15)(-44+k)]

= 4(-6) -2(15k-156) +4(7k-68)

= -2k+16

Since the matrix is singular det(M)=0

-2k+16 =0

k=8