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Prove: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,...

Prove: `|[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3`

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Show that: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

Prove that: |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|= 2(a+b+c)^3

Prove that: |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]|=|[a^2+1,b^2,c^2],[a^2,b^2+1,c^2],[a^2,b^2,c^2+1]|=1+a^2+b^2+c^2

Prove that: |[a+b, b+c, c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]|=2|[a,b,c],[b,c,a],[c,a,b]|

Without expanding the determinant, prove that |[a,a^2,bc],[b,b^2,ca],[c,c^2,ab]| = |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

Prove that: {:|(a^2,a,b+c),(b^2,b,c+a),(c^2,c,ab)| = -(a+b+c)(a-b)(b-c)(c-a)

Prove that: {:|(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,)|=(a+b)+c)(a^2+b^2+c^2)

ARIHANT MATHS-DETERMINANTS -Exercise (Subjective Type Questions)
  1. Prove that |{:(b+c,a,a),(b,c+a,b),(c,c,a+b):}| = 4 abc

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  2. Prove: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

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  3. Find the value of determinant |[sqrt((13))+sqrt(3),2sqrt(5),sqrt(5)],[...

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  4. Find the value of the determinant |(bc,ca, ab),( p, q, r),(1, 1, 1)|,w...

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  5. Without expanding the determinant at any stage prove that |{:(-5,3+5i...

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  6. Prove without expansion that |{:(a h+bg,g,ab+ch), (bf+ba,f,hb+bc), (af...

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  7. In a triangleABC, if |(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB...

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  8. The value of |{:(betagamma,betagamma'+beta'gamma,beta'gamma'),(gammaal...

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  9. If y=(u)/(v), where u & v are functions of 'x' show that v^(3)(d^(2)y)...

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  10. Show that the determinant Delta(x) given by Delta(x) = |{:(sin(x+al...

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  11. Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)C(3)),(.^(y)C(1),,.^(y)C(2),,....

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  12. Find maximum value of f(x)=|{:(1+sin^(2)x,cos^(2)x,4sin2x),(sin^(2)...

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  13. If f(x) = |[x^2-4x+6,2x^2+4x+10,3x^2-2x+16],[x-2,2x+2,3x-1],[1,2,3]| t...

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  14. If |A| = 2 and A = | (2x, 6) , (5x, 1)| then find the value of x

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  15. Find the value of t for which the following system of equations has a ...

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  16. Find dy/dx if y=13x-y^2

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  17. If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx ...

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