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10.6 Determinants and Cramer’s Rule

Focus on $2\times 2$ determinant and cramer rule condition.

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01Determinant of a 2 × 2 matrixWorked steps · five questions 02Determinant of a 3 × 3 matrix (cofactor expansion)Worked steps · five questions 03Cramer's RuleWorked steps · five questions

Lesson brief and rules

10.6 Determinants and Cramer’s Rule

The determinant of $\begin{bmatrix}a & b \\ c & d\end{bmatrix}$ is $ad-bc$ .

Worked example

1

01 / Find

\det \begin{bmatrix}3 & 5 \\ 4 & 7\end{bmatrix}

02 /

ad-bc=3(7)-5(4)=1

03 / Answer:

1

Worked example 2 · Cramer rule condition

When can Cramer’ $s$ Rule yield a unique solution?

Cramer’ $s$ Rule divides by the coefficient determinant. Answer: Coefficient determinant nonzero

15 questions covering every idea, with a worked answer for each.Start practice ↗

Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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10.6 Determinants and Cramer’s Rule

Ideas in this lesson

10.6 Determinants and Cramer’s Rule