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Ch. 6 - Matrices and Determinants
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 6 - Matrices and DeterminantsProblem 7
Chapter 7, Problem 7

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

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1
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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
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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.
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Interval Notation

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.
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Textbook Question

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Find the products AB and BA to determine whether B is the multiplicative inverse of A.

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