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Given the equations x=cy+bz, y=az+cx a...

Given the equations
x=cy+bz, y=az+cx and z=bx+ay
where x,y and z are not all zero, prove that `a^2+b^2+c^2+2abc=1` by determinant method.

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ARIHANT PUBLICATION-DETERMINANTS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS (EXERCISE 5(A))
  1. Prove that the following. [[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+...

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  2. Show that: abs((a,a^2,a^3),(b,b^2,b^3),(c,c^2,c^3))=abc(a-b)(b-c)(c-a)

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  3. Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4ab

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  4. Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+...

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  5. Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]]=(b-c)(c-a...

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  6. Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=...

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  7. Prove that the following. |[(v+w)^2,u^2,u^2],[v^2,(w+u)^2,v^2],[w^2,w...

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  8. Factorize the following. [[x+a,b,c],[b,x+c,a],[c,a,x+b]]

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  9. Factorize the following. [[a,b,c],[b+c,c+a,a+b],[a^2,b^2,c^2]]

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  10. Factorize the following. [[x,2,3],[1,x+1,3],[1,4,x]]

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  11. Show that by eliminating alpha and beta from the equations. aialpha+...

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  12. Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]]=0

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  13. Prove the following : [[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]]-(5x+4)(4-x...

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  14. Prove the following : [[sinalpha,cosalpha,cos(alpha+delta)],[sinbeta,c...

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  15. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

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  16. Prove that the points : (x1,y1),(x2,y2),(x3,y3) are collinear if [[x...

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  17. If A+B+C = pi, prove that [[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,c...

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  18. Eliminate x,y,z from a=x/y-z, b=y/z-x, c=z/x-y

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  19. Given the equations x=cy+bz, y=az+cx and z=bx+ay where x,y and z a...

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  20. If ax+hy+g=0, hx+by+f=0 and gx+fy+c=lamda, find the value of lamda in ...

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