Questions: [1 3 7 4; 0 5 9 6; 0 0 2 8; 0 0 0 10] is the matrix invertible

Solution Steps

To determine if a matrix is invertible, we need to check if its determinant is non-zero. For an upper triangular matrix, the determinant is the product of its diagonal elements. If the product is non-zero, the matrix is invertible.

The given matrix is

\[ A = \begin{bmatrix} 1 & 3 & 7 & 4 \\ 0 & 5 & 9 & 6 \\ 0 & 0 & 2 & 8 \\ 0 & 0 & 0 & 10 \end{bmatrix} \]

For an upper triangular matrix, the determinant is the product of the diagonal elements. Thus, we calculate:

\[ \text{det}(A) = 1 \cdot 5 \cdot 2 \cdot 10 = 100 \]

Since the determinant is \(100\), which is non-zero, the matrix \(A\) is invertible.

Final Answer