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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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evaluate: |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|

Using the properties of determinants, prove that following |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c)^3

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

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

If |(a-b-c, 2a, 2a),(2b, b-a-c, 2b),(2c, 2c, c-a-b)|=(a+b+c)(x+a+b+c)^2 then the value of x is equal to (A) -2(a+b+c) (B) a+b+c (C) -(a+b+c) (D) 2(a+b+c)

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

Prove the following, using properties of determinants: |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|=2(a+b+c)^3

Using properties of determinant, prove that |(2a, a-b-c, 2a), (2b, 2b, b-c-a), (c-a-b,2c,2c)|=(a+b+c)^(3) .

Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c)(c+a)

Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c)(c+a)

ARIHANT MATHS ENGLISH-DETERMINANTS -Exercise (Subjective Type Questions)
  1. Prove that |{:(b+c,c,b),(c,c+a,a),(b,a,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+bgga b+c h bf+b afh b+b c af+b cc bg...

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

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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. Show that in general there are three values of t for which the followi...

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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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