Evaluate each determinant in Exercises 1–10. ∣5723∣\begin{vmatrix} 5 & 7 \\ 2 & 3 \end{vmatrix}5273

Ch. 6 - Matrices and Determinants

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Blitzer 8th Edition

Ch. 6 - Matrices and Determinants

문제 1

7장, 문제 1

Evaluate each determinant in Exercises 1–10.
$\begin{vmatrix}\)5 & 7 \\2 & 3\(\end{vmatrix}$

검증된 단계별 안내

Identify the matrix given as a 2x2 matrix: $\begin{bmatrix} 5 & 7 \\ 2 & 3 \end{bmatrix}$.

Recall the formula for the determinant of a 2x2 matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$, which is $ad - bc$.

Assign the values from the matrix to the variables: $a = 5$, $b = 7$, $c = 2$, and $d = 3$.

Substitute these values into the determinant formula: $5 \times 3 - 7 \times 2$.

Simplify the expression to find the determinant value (do not calculate the final number here).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

59s

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Determinant of a 2x2 Matrix

The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated as ad - bc. It is a scalar value that provides important information about the matrix, such as whether it is invertible. For the given matrix [[5, 7], [2, 3]], the determinant is (5)(3) - (7)(2).

Matrix Notation and Elements

A matrix is a rectangular array of numbers arranged in rows and columns. Each element is identified by its row and column position. Understanding how to read and identify elements in a matrix is essential for performing operations like finding determinants.

Properties and Applications of Determinants

Determinants help determine if a matrix is invertible (non-zero determinant) and are used in solving systems of linear equations, finding area or volume transformations, and understanding linear transformations. Recognizing these applications helps contextualize why calculating determinants is important.

Evaluate each determinant in Exercises 1–10. ∣5723∣\(\begin{vmatrix}\)5 & 7 \\2 & 3\(\end{vmatrix}\)5273