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Chapter 3: Problem 41

Find the determinant of the triangular matrix. $$\left[\begin{array}{rrr} -2 & 0 & 0 \\ 4 & 6 & 0 \\ -3 & 7 & 2 \end{array}\right]$$

Short Answer

Expert verified
Accordingly, the determinant of the given matrix is -24.

Step by step solution

01

Identifying the Matrix type

The given matrix is an upper triangular matrix. For an upper triangular matrix, all elements below the diagonal are zero.
02

Using the Property of Triangular Matrix

The determinant of a triangular matrix is the product of the elements on its main diagonal.
03

Calculating the Determinant

The elements on the main diagonal of the given matrix are -2, 6, 2. The determinant is therefore equal to \(-2 \times 6 \times 2 = -24\).

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Most popular questions from this chapter

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