Unless otherwise specified, assume that all matrices in these exercises are n x n. Invertible

# Unless otherwise specified, assume that all matrices in these exercises are n x n. Invertible

A
45 points

Unless otherwise specified, assume that all matrices in these exercises are n n. Determine which of the matrices in Exercises 1–10 are invertible. Use as few calculations as possible. Justify your answers.

$$\begin{bmatrix}1 & 3 & 7 & 4\\0 & 5 & 9 & 6\\0 & 0 & 2 & 8\\0 & 0 & 0 & 10\end{bmatrix}$$

Unless otherwise

8.7k points

The matrix is invertible by the inverse matrix theorem, which in this case says it is invertible since it has 4 pivot positions.

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