If $x - 2x + 3x = 100$, what is the value of $x$?
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Answer:
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