Question

In Problems 7-14, find the value of each delerminant. . $\left|\begin{array}{ll}-4 & 2 \\ -5 & 3\end{array}\right|$

   In Problems 7-14, find the value of each delerminant.
 . $\left|\begin{array}{ll}-4 & 2 \\ -5 & 3\end{array}\right|$

Precalculus: pearson new international edition

Precalculus: pearson new international edition

Michael Sullivan 9th Edition

Chapter 11, Problem 10

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Step 1

The determinant of a 2x2 matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is calculated as $ad - bc$. For the matrix given, $\begin{bmatrix} -4 & 2 \\ -5 & 3 \end{bmatrix}$, we identify $a = -4$, $b = 2$, $c = -5$, and $d = 3$. Show more…

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In Problems 7-14, find the value of each delerminant. . $\left|\begin{array}{ll}-4 & 2 \\ -5 & 3\end{array}\right|$

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Key Concepts

Determinant

A determinant is a scalar attribute calculated from the entries of a square matrix. It helps in analyzing the matrix's properties, including invertibility and the scaling factor applied during a linear transformation.

2x2 Matrix Determinant Formula

For a matrix with two rows and two columns, the determinant is computed using the formula ad - bc, where a, b, c, and d are the elements of the matrix. This concise formula is the foundation for understanding determinants in linear algebra.

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