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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define what it means for a matrix to have an inverse.
💡 Hint: Think about the identity matrix.
Question 2
Easy
What is the condition for a matrix to be non-singular?
💡 Hint: Recall the property of determinants.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the formula for the inverse using the adjoint method?
- A⁻¹ = adj(A)/det(A)
- A⁻¹ = det(A)/adj(A)
- A⁻¹ = A*adj(A)
💡 Hint: Recall the roles of adjugate and determinant.
Question 2
True or False: A singular matrix has an inverse.
- True
- False
💡 Hint: Think about the determinant's role.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the matrix A = \( \begin{bmatrix} 2 & 4 \ 1 & 3 \end{bmatrix} \), find the inverse using both methods: adjoint and Gauss-Jordan.
💡 Hint: Calculate determinant first, for both methods.
Question 2
For a 4x4 matrix B, apply Gauss-Jordan elimination and find the inverse, showing each step explicitly. Consider B = \( \begin{bmatrix} 1 & 2 & 3 & 4 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{bmatrix} \).
💡 Hint: Use row swaps and scaling as necessary.
Challenge and get performance evaluation