Mathematics for Computer Scientists 2 (COMP1045 UNMC) (SPM1 24-25)
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Elementary row operations include:
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The determinant of A in LU = A is equal to:
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Gaussian elimination helps determine the rank of a matrix by:
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For a system to be compatible, the rank of the augmented(complete) matrix must be:
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In a system of linear equations, the rank of complete matrix is equal to the rank of coefficient matrix equal to the number of variables is less than number of linear equations. The system has:
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The trivial solution of a homogeneous system always exists, but its significance is that:
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If a homogeneous system has more variables than equations, it always has:
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The classification of a system as compatible or incompatible depends on:
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A square matrix has an inverse if and only if its determinant is:
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For a system to be inconsistent, the rank of the augmented matrix must be:
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