MATH1002 Lecture Notes - Lecture 13: Invertible Matrix, Elementary Matrix, Diagonal Matrix
20 Aug 2018
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Document Summary
Going through the first row, multiply each value by the determinant of its corresponding smaller matrix, alternating adding and subtracting. To get the corresponding smaller matrix, it is a 2 x 2 matrix formed by removing a row and a column from the original matrix - it is called the minor. The minor matrix a is formed by removing the first row and second. The alternating signs: you alternate the signs for each term in the determinant calculation. Using [(-1)i+j] ij n det(a) = ( 1)i+j j=1 det(i) = 1 n. Aij det(a)ij the expansion over row i. A matrix with only zeroes below the diagonal will be the the product of the diagonal terms. Finding determinant using elementary row operations: if you swap two rows, you swap the sign of the determinant. |det(a)| is the volume of the parallelogram formed by the column vectors of the matrix.
