- #1

TanWu

- 17

- 5

- Homework Statement
- (a) Show that a matrix ##\left(\begin{array}{ll}e & g \\ 0 & f\end{array}\right)## has determinant equal to the product of the elements on the leading diagonal. Can you generalise this idea to any ##n \times n## matrix?

- Relevant Equations
- ##\left(\begin{array}{ll}e & g \\ 0 & f\end{array}\right)##

I have a doubt about this problem.

(a) Show that a matrix ##\left(\begin{array}{ll}e & g \\ 0 & f\end{array}\right)## has determinant equal to the product of the elements on the leading diagonal. Can you generalize this idea to any ##n \times n## matrix? The first part is simple, it is just ef.

I have a doubt about what ##n \times n## matrix they want generalized too, for example do they want a upper triangular ##n \times n## matrix like the one the author as written or a lower triangular, or general matrix, etc.

I express gratitude to those who help.

(a) Show that a matrix ##\left(\begin{array}{ll}e & g \\ 0 & f\end{array}\right)## has determinant equal to the product of the elements on the leading diagonal. Can you generalize this idea to any ##n \times n## matrix? The first part is simple, it is just ef.

I have a doubt about what ##n \times n## matrix they want generalized too, for example do they want a upper triangular ##n \times n## matrix like the one the author as written or a lower triangular, or general matrix, etc.

I express gratitude to those who help.