Using the property of determinant and without expanding prove that \(\left| {\begin{array}{*{20}{c}} x&a&{x + a} \\ y&b&{y + b} \\ z&c&{z + c} \end{array}} \right| = 0\)
If A = \(\left[\begin{array}{lll} {1} & {3} & {3} \\ {1} & {4} & {3} \\ {1} & {3} & {4} \end{array}\right]\)then verify that A adj A = | A| I. Also find A–1.
The sum of three numbers is 6. If we multiply third number by 3 and add second number to it, we get 11. By adding first and third number, we get double of the second number. Represent it algebraically and find the numbers using matrix method.