Find the determinant of the matrix $$ H=\left[\begin{array}{lll}y & d & c \ 0 & z & b \ 0 & 0 & x\end{array} ight] $$

Question

Find the determinant of the matrix $$ H=\left[\begin{array}{lll}y & d & c \ 0 & z & b \ 0 & 0 & x\end{array}ight] $$

UpStudy AI · Accepted Answer

The matrix is given as

$$
H=\begin{bmatrix}
y & d & c \
0 & z & b \
0 & 0 & x
\end{bmatrix}.
$$

Since $$ H $$ is an upper triangular matrix (all entries below the main diagonal are zero), its determinant is the product of the diagonal elements. That is,

$$
\det(H) = y \cdot z \cdot x.
$$
The determinant of matrix $$ H $$ is $$ y \times z \times x $$.

Find the determinant of the matrix

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