Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. [Start 4 By 4 Matrix 1st Row 1st Column 4 2nd Column 5 3rd Column 7 4st Column 5 2nd Row 1st Column 0 2nd Column 1 3rd Column 4 4st Column 6 3rd Row 1st Column 0 2nd Column 0 3rd Column 3 4st Column 8 4st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 1 EndMatrix ]

Yes, it is invertible

Step-by-step explanation:

We need to find in the matrix determinant is different from zero, since iif it is, that the matrix is invertible.

Let's use co-factor expansion to find the determinant of this 4x4 matrix, using the column that has more zeroes in it as the co-factor, so we reduce the number of determinant calculations for the obtained sub-matrices.We pick the first column for that since it has three zeros!

Then the determinant of this matrix becomes:

And the determinant of these 3x3 matrix is very simple because most of the cross multiplications render zero:

Therefore, the Det of the initial matrix is : 4 * 3 = 12

and then the matrix is invertible

191 students play sports and ninety-seven 10th graders were surveyed.

step-by-step explanation: