The formula det A = for the determinant of an n x n matrix and A1,1C1,1 + A1,2C1,2 + + A1, C1,n • reduces the calculation of the determinant of a 2 x 2 matrix into a linear combination of the determinants of two 1 x 1 matrices. • reduces the calculation of the determinant of a 3 × 3 matrix into a linear combination of the determinants of six 1 x 1 matrices. • reduces the calculation of the determinant of a 4 × 4 matrix into a linear combination of the determinants of twenty-four 1 × 1 matrices. a. reduces the calculation of the determinant of a 5 x 5 matrix into a linear combination of the determinants of 1 x 1 matrices. b. reduces the calculation of the determinant of an n x n matrix into a linear combination of the determinants of 1 x 1 matrices.
The formula det A = for the determinant of an n x n matrix and A1,1C1,1 + A1,2C1,2 + + A1, C1,n • reduces the calculation of the determinant of a 2 x 2 matrix into a linear combination of the determinants of two 1 x 1 matrices. • reduces the calculation of the determinant of a 3 × 3 matrix into a linear combination of the determinants of six 1 x 1 matrices. • reduces the calculation of the determinant of a 4 × 4 matrix into a linear combination of the determinants of twenty-four 1 × 1 matrices. a. reduces the calculation of the determinant of a 5 x 5 matrix into a linear combination of the determinants of 1 x 1 matrices. b. reduces the calculation of the determinant of an n x n matrix into a linear combination of the determinants of 1 x 1 matrices.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The formula
det A = A1,1C1,1 + A1,2C1,2+ + A1,nC1,n
for the determinant of an n x n matrix
and
• reduces the calculation of the determinant of a 2 × 2 matrix into a linear combination of the
determinants of two 1 x 1 matrices.
• reduces the calculation of the determinant of a 3 × 3 matrix into a linear combination of the
determinants of six 1 × 1 matrices.
• reduces the calculation of the determinant of a 4 × 4 matrix into a linear combination of the
determinants of twenty-four 1 × 1 matrices.
a. reduces the calculation of the determinant of a 5 x 5 matrix into a linear combination of the
determinants of
1 x 1 matrices.
b. reduces the calculation of the determinant of an n x n matrix into a linear combination of the
determinants of
1 x 1 matrices.
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