Answered: Using properties of determinants, prove…

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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Ex: Prove without open the determinant that, (using determinant properties)

Determinant Properties:

1- If two rows or columns of a matrix are identical, the
the determinant is zero.
2- The determinant of a matrix is the sum of the products of the
elements of the ith row or column by their cofactors, for any i.
3- The determinant of the transpose of a matrix is equal to the
original determinant |A|=|A|^T.
4- If each element of some row or column of a matrix is multiplied
by a constant c, the determinant is multiplied by c.

5- If the matrix is an upper or a lower triangular matrix, the determinant
of the matrix is the product of the elements on the main diagonal.

Using properties of determinants, prove without open the determinant that:
b.
a
a
c -(a-bXb-cXc-aXa+b+c)
b+c c+a a+b

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