Applications of Matrices and Determinants — Practice Quiz
ICSE · Class 12 · Mathematics
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Quick Quiz: Applications of Matrices and Determinants
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A system of equations AX = B is said to be consistent if:
A system of equations AX = B is said to be inconsistent if:
If |A| ≠ 0, the system AX = B has:
The unique solution of AX = B (when |A| ≠ 0) is given by:
Sample Questions
A system AX = O (where O is the zero matrix) is called:
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Homogeneous
A system is homogeneous when all constant terms are zero, i.e., B = O.
A homogeneous system AX = O is always consistent.
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True
X = O (trivial solution) always satisfies AX=O. So a homogeneous system always has at least one solution and is therefore always consistent.
The formula for A⁻¹ in terms of adj A is:
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A⁻¹ = adj A / |A|
A⁻¹ = (adj A)/|A|. This requires |A| ≠ 0.
If C_ij is the cofactor of element a_ij, then the cofactor C_ij equals:
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(−1)^(i+j) × M_ij
Cofactor = (−1)^(i+j) × minor. The sign alternates in a checkerboard pattern.
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