21.4.3 - Methods to Find Inverse
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Practice Questions
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Define what it means for a matrix to have an inverse.
💡 Hint: Think about the identity matrix.
What is the condition for a matrix to be non-singular?
💡 Hint: Recall the property of determinants.
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Interactive Quizzes
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What is the formula for the inverse using the adjoint method?
💡 Hint: Recall the roles of adjugate and determinant.
True or False: A singular matrix has an inverse.
💡 Hint: Think about the determinant's role.
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Challenge Problems
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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.
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.
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