Inverse of a Matrix and Its Applications
Telangana Open School (TOSS) · Class 12 · Mathematics
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Quick Quiz: Inverse of a Matrix and Its Applications
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If a matrix A has determinant zero, then it is called:
The inverse of a matrix exists only if the matrix is:
For a 2×2 matrix A, the adjoint is obtained by:
If A is a square matrix and |A| ≠ 0, then A⁻¹ is given by:
Sample Questions
The system of equations AX = B has a unique solution if:
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|A| ≠ 0
If the coefficient matrix A has non-zero determinant, the system has a unique solution given by X = A⁻¹B.
The minor M₁₂ of the matrix [[1,2],[3,4]] is:
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3
Minor M₁₂ is the determinant obtained by deleting row 1 and column 2, which leaves element 3. So M₁₂ = 3.
The cofactor C₁₁ of the matrix [[2,5],[4,3]] is:
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3
C₁₁ = (-1)¹⁺¹ × M₁₁ = 1 × |3| = 3.
If A is a 2×2 matrix and |A| = 5, then |Adj A| equals:
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5
For a 2×2 matrix, |Adj A| = |A|^(2-1) = |A| = 5.
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