Evaluate each determinant in Exercises 1–10.∣121218−34∣\begin{vmatrix} \frac{1}{2} & \frac{1}{2} \\ \frac{1}{8} & - \frac{3}{4} \end{vmatrix}218121−43

Ch. 6 - Matrices and Determinants

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Blitzer 8th Edition

Ch. 6 - Matrices and Determinants

문제 9

7장, 문제 9

Evaluate each determinant in Exercises 1–10. $\begin{vmatrix}\) $\frac{1}{2}$ & $\frac{1}{2}$ \\ $\frac{1}{8}$ & - $\frac{3}{4}$ \(\end{vmatrix}$

검증된 단계별 안내

Identify the determinant of the 2x2 matrix given as: $\begin{pmatrix} \frac{1}{2} & \frac{1}{2} \\ \frac{1}{8} & -\frac{3}{4} \end{pmatrix}$.

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

Assign the values: $a = \frac{1}{2}$, $b = \frac{1}{2}$, $c = \frac{1}{8}$, and $d = -\frac{3}{4}$.

Calculate the product $ad = \left(\frac{1}{2}\right) \times \left(-\frac{3}{4}\right)$ and the product $bc = \left(\frac{1}{2}\right) \times \left(\frac{1}{8}\right)$.

Subtract the two products to find the determinant: $ad - bc$.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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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 of the matrix and is essential in solving systems of linear equations.

Fraction Arithmetic

When working with fractions in matrices, it is important to correctly perform multiplication and subtraction. Multiplying fractions involves multiplying numerators and denominators, while subtraction requires a common denominator.

Simplification of Expressions

After calculating the determinant expression, simplifying the resulting fraction or mixed number is necessary. This involves reducing fractions to their simplest form to provide a clear and final answer.

Evaluate each determinant in Exercises 1–10.∣121218−34∣\(\begin{vmatrix}\) \(\frac{1}{2}\) & \(\frac{1}{2}\) \\ \(\frac{1}{8}\) & - \(\frac{3}{4}\) \(\end{vmatrix}\)218121−43

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Determinant of a 2x2 Matrix

Fraction Arithmetic

Simplification of Expressions

Evaluate each determinant in Exercises 1–10. $\begin{vmatrix}\) \(\frac{1}{2}\) & \(\frac{1}{2}\) \\ \(\frac{1}{8}\) & - \(\frac{3}{4}\) \(\end{vmatrix}$