Compute the determinants using a cofactor expansion across the first row. Also compute the determinant by a cofactor expansion down the second column. [ 0 4 1
5 −3 0
2 3 1 ]

Step-by-step explanation:

Given the 3* 3 matrices , to compute the determinant using the first row means using the row values [0 4 1 ] to compute the determinant. Note that the signs on the values on the first row are +0, -4 and +1

Calculating the determinant;

The determinant is 1 using the first row as co-factor

Similarly, using the second column as the cofactor, the determinant will be expressed as shown;

Note that the signs on the values are -4, +(-3) and -3.

Calculating the determinant;

The determinant is also 1 using the second column as co factor.

It can be concluded that the same value of the determinant will be arrived at no matter the cofactor we choose to use.

a) false; the points do not have to be in a straight line.

step-by-step explanation:

the points could be in the shape of a triangle

b is incorrect

c is incorrect because it is saying the immediately don't form one when they are capable of doing so

d is incorrect