Question

Are the following matrices invertible? Choose [[8,7],[-16,-14]] Choose [[-16,7],[0,0]] Choose [[-3,4],[-4,-3]] Choose [[-5,-5],[-2,0]]

Answer 1

Out of the matrices provided, only the third [ [ -3,4], [ -4,-3] ] and fourth [ [ -5,-5], [ -2,0 ] ] matrices are invertible, as they have non-zero determinants.

Step-by-step explanation:

Whether or not the following matrices are invertible can be determined by calculating the determinant of each matrix. A matrix is invertible if its determinant is not equal to zero.

• [[8,7],[-16,-14]]: The determinant is (8*(-14)) - (7*(-16)) = -112 + 112 = 0, so this matrix is not invertible.
• [[-16,7],[0,0]]: The determinant is (-16*0) - (7*0) = 0, so this matrix is not invertible.
• [[-3,4],[-4,-3]]: The determinant is ((-3)*(-3)) - (4*(-4)) = 9 - (-16) = 25, so this matrix is invertible.
• [[-5,-5],[-2,0]]: The determinant is ((-5)*0) - (-5*(-2)) = 0 - (-10) = 10, so this matrix is invertible.

So, out of the matrices given, only the third and fourth ones are invertible as they have non-zero determinants.