Understanding Determinant of a Matrix
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Beginner
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Beginner Explanation
The determinant of a 2x2 matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ is found using $ad - bc$.
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Practice Problems
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1
Quick Quiz
Single Choice Quiz
Beginner
Calculate the determinant of $\begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix}$.
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2
Real-World Problem
Question Exercise
Intermediate
Teenager Scenario
You are planning a school project that involves solving the following system of equations: 2x + y = 3; 3x + 4y = 5. Determine if the system has a unique solution by calculating the determinant of the coefficient matrix.
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3
Thinking Challenge
Thinking Exercise
Intermediate
Think About This
Explain why a zero determinant indicates no unique solution for a system of linear equations.
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4
Challenge Quiz
Single Choice Quiz
Advanced
Given a matrix $\begin{pmatrix} x & 3 \\ 2 & 5 \end{pmatrix}$, for what value of $x$ is the determinant zero?
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Recap
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