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Using properties of determinants prove ...

Using properties of determinants prove the
following.
`abs[[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4abc`

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Using properties of determinants prove the following. abs[[1,a,bc],[1,b,ca],[1,c,ab]]=(a-b)(b-c)(c-a)

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using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a) .

Using properties of determinants, show that abs[[a,a^2,b+c],[b,b^2,c+a],[c,c^2,a+b]]=(b-c)(c-a)(a-b)(a+b+c)

By using properties of determinants, prove that |[-a^2,ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

By using properties of determinants, prove that |[0,a ,-b],[-a,0,-c],[b,c,0]|=0

Prove that abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

Using properties of determinants, prove that |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]| = 3(a+b+c)(ab+bc+ca)

Without expanding the determinant prove the following. |[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]|=0

BODY BOOKS PUBLICATION-DETERMINANTS-EXERCISE
  1. Arjun' purchased 3 pens,2 purses and 1 instrument box and pays Rs. 4...

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  2. Write the value of x+y+z, if [(1,0,0),(0,1,0),(0,0,1)][(x),(y),(z)]=[(...

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  3. Using properties of determinants prove the following. abs[[b+c,a,...

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  4. Consider the points (b,c+a),(c,a+b) and (a,b+c). Find the area of the ...

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  5. Consider the points (b,c+a),(c,a+b) and (a,b+c). Are the given points ...

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  6. If Delta=[(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)] Perform R1rarrR1+...

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  7. If Delta=[(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)]Perform R1rarrR1+R...

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  8. Using properties of determinants prove the following. abs[[a-b-c,...

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  9. Given Delta=[(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)] Express given ...

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  10. Show that abs[[a+b,b+c,c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]]=2abs[[a,b,c],...

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  11. Find the equation of line joining (1,2) and (3,6) using determinants.

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  12. Prove that |[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]| is...

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  13. Prove that |[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]| is...

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  14. using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],...

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  15. If A=[[2,-3,5],[3,2,-4],[1,1,-2]] Find A^-1

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  16. If A=[[2,-3,5],[3,2,-4],[1,1,-2]] Using it solve the system of equat...

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  17. prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

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  18. if A=[[1,-1,2],[0,2,-3],[3,-2,4]] B=[[-2,0,1],[9,2,-3],[6,1,-2]] Prov...

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  19. if A=[[1,-1,2],[0,2,-3],[3,-2,4]] B=[[-2,0,1],[9,2,-3],[6,1,-2]] ...

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  20. If A=[[a,1],[1,0]] is such that A^2=I then a equals

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