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AAKASH SERIES-MATRICES -Exercise - 3.4 (Short Answer Questions)
- Show that |{:(a-b-c," "2a," "2a),(" "2b,b-c-a," "2b),(" "2c," "2...
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- Show that |{:(bc,b+c,1),(ca,c+a,1),(ab,a+b,1):}|=(a-b)(b-c)(c-a)
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- Show that |(b+c,c+a,a+b),(a+b,b+c,c+a)(a,b,c)|=a^(3)+b^(3)+c^(3)-3abc.
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- Show that |{:(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab):}|=0
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- Show that |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3
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- |(1+a,b,c),(a,1+b,c),(a,b,1+c)|=
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- |(a^(2)+2a,2a+1,1),(2a+1,a+2,1),(3,3,1)|
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- Show that |{:(x,a,a),(a,x,a),(a,a,x):}|=(x+2a)(x-a)^2
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- Without expanding the determinant, prove that (i) |{:(a,a^(2),bc),(b,b...
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- IFDelta1=|{:(1,cosalpha,cosbeta),(cosalpha,1,coygamma),(cosbeta,cosgam...
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- If Delta(1)=|{:(a(1)^(2)+b(1)+c(1),a(1)a(2)|b(2)|c(2),a(1)a(3)+b(3)+c(...
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