Mathematics, 06.06.2021 18:30 tammycute01

Without expanding the determinants, show that the value of exach of the following determinants is zero. 1) $\left[\begin{array}{ccc}1&w&w^{2} \\w&w^{2} &1\\w^{2} &1&w^{2} \end{array}\right]$
2) $\left[\begin{array}{ccc}1&bc&a(b+c)\\1&ca&b(c+a)\\1&ab&c(a+b)\end{array}\right]$
3) $\left[\begin{array}{ccc}1&bc&bc(b+c)\\1&ca&ca(c+a)\\1&ab&ab(a+b)\end{array}\right]$
4) $\left[\begin{array}{ccc}(a-b)&(b-c)&(c-a)\\(b-c)&(c-a)&(a-b)\\(c-a)&(a-b)&(b-c)\end{array}\right]$

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Without expanding the determinants, show that the value of exach of the following determinants is zero. 1) 2) 3)4)

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