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Using the property of determinants and w...

Using the property of determinants and without expanding, prove that `|(2,7,65), (3,8,75), (5,9,86)|=0`

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Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(2,7,65),(3,8,75),(5,9,86):}|=0

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(0,a,-b),(-a,0,-c),(b,c,0):}|=0

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,x,x^2),(x^2,1,x),(x,x^2,1):}|=(1-x^3)^2

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(y+k,y,y),(y,y+k,y),(y,y,y+k):}|=k^2(3y+k)

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,1,1),(a,b,c),(a^3,b^3,c^3):}|=(a-b)(b-c)(c-a)(a+b+c)