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

Ch. 6 - Matrices and Determinants

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Blitzer 8th Edition

Ch. 6 - Matrices and Determinants

문제 7

7장, 문제 7

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

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Identify the matrix given as a 2x2 matrix: $\begin{bmatrix} -5 & -1 \\ -2 & -7 \end{bmatrix}$.

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: $a = -5$, $b = -1$, $c = -2$, and $d = -7$.

Substitute these values into the determinant formula: $(-5)(-7) - (-1)(-2)$.

Simplify the expression step-by-step to find the determinant value.

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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. This scalar value helps determine properties like invertibility and area scaling in transformations.

Matrix Notation and Elements

Understanding matrix notation involves recognizing the position of elements: 'a' and 'b' in the first row, 'c' and 'd' in the second. Correctly identifying these values is essential for accurate determinant calculation.

Application of Determinants in Problem Solving

Evaluating determinants is a fundamental skill in algebra used to solve systems of equations, find inverses, and analyze linear transformations. Mastery of this concept aids in broader mathematical problem solving.

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