Show that |(b+c,c+a,a+b),(a+b,b+c,c+a)(a...

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 |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^(3) .

Show that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=2|{:(a,b,c),(b,c,a),(c,a,b):}|

Without expanding the determinant show that |(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2|(a,b,c),(b,c,a),(c,a,b)|

Show that |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0

If abc!=0 and if |(a,b,c),(b,c,a),(c,a,b)|=0 then (a^(3)+b^(3)+c^(3))/(abc)=

Show that |{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(2),b^(3),c^(3)):}|=abc(a-b)(b-c)(c-a)

SRISIRI PUBLICATION-MATRICES-SHORT ANSWER TYPE QUESTIONS

Show that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)
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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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Prove that |{:(y+z,x,x),(y,z+x,y),(z,z,x+y):}|=4xyz
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IF |{:(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^3):}|=0 , then show that ...
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Without expanding the determinant , prove that |{:(a,a^2,bc),(b,b^2,ca...
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Without expanding the determinant , prove that |{:(ax,by,cz),(x^2,y^2,...
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Without expanding the determinant, prove that |{:(1,bc,b+c),(1,ca,c+a)...
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Show that |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0
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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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Let A and B be invertible matrices then prove that (AB)^-1=B^-1A^-1.
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Find the adjoint and the inverse of the matrix A=[{:(1,3,3),(1,4,3),(1...
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Show that the matrix A=[{:(1,2,1),(3,2,3),(1,1,2):}] is non-singular a...
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IF abc ne 0, find the inverse of [{:(a,0,0),(0,b,0),(0,0,c):}]
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IF A=[{:(-1,-2,-2),(2,1,-2),(2,-2,1):}] then show that adj A=3A^T. Als...
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IF A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}] then show that A^-1=A^3.
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IF 3A=[{:(1,2,2),(2,1,-2),(-2,2,-1):}] then show that A^-1=A'.
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Find the rank of A=[{:(0,1,2),(1,2,3),(3,2,1):}] using elementary tran...
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Find the rank of A=[{:(1,2,0,-1),(3,4,1,2),(-2,3,2,5):}] using element...
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If A is a non-singular matrix then prove that A^(-1) = (adjA)/(|A|).
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