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Ch. 6 - Matrices and Determinants
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 6 - Matrices and DeterminantsProblema 9
Capitolo 7, Problema 9

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

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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: $ad - bc$.

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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.
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Determinants of 2×2 Matrices

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.
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Arithmetic Sequences - General Formula

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.
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Introduction to Algebraic Expressions
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