Question

Conider matrice C and D. C = [-3 9 -2 6] D = [-9 3 -12 -4] The determinant of matrix C i ____ the determinant of matrix D, and ____ an invere matrix

Answer 1

The determinant of matrix C is greater than the determinant of matrix D. Matrix C has an inverse, but it is not known if matrix D has an inverse.

Step-by-step explanation:

The determinant of matrix C is -3*(-4)-9*(-12)-2*(-9)-6*(-4) = 78.

The determinant of matrix D is -9*(-12)-3*(-4)-12*(-9)-4*(-4) = 12.

Therefore, the determinant of matrix C is greater than the determinant of matrix D.

As for the inverse matrix, we need to determine if the determinant is nonzero. Since the determinant of matrix C is nonzero, it has an inverse. However, this information is not provided for matrix D.

Answer 2

The determinant of matrix C is not equal to the determinant of matrix D, and matrix C does not have an inverse because its determinant is zero.

Step-by-step explanation:

To determine if matrices have inverses, we can calculate their determinants. The determinants can also tell us if matrices are proportional if their determinants are multiples of each other. In this case, we have the matrix C = [-3 9 -2 6] and matrix D = [-9 3 -12 -4]. The determinant of a 2x2 matrix A = [a b; c d] is calculated as det(A) = ad - bc.

So, for matrix C, the determinant is (-3)(6) - (9)(-2) which equals -18 + 18 = 0.

For matrix D, the determinant is (-9)(-4) - (3)(-12) which equals 36 + 36 = 72.

Thus, the determinant of matrix C is not equal to the determinant of matrix D, and since the determinant of matrix C is zero, it does not have an inverse matrix because only non-singular matrices (matrices with a non-zero determinant) have inverses.