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evaluate | [1,x,y],[1,x+y,y],[1,x,x+y] ...

evaluate ` | [1,x,y],[1,x+y,y],[1,x,x+y] | `

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Evaluate |[x, y, x+y],[ y, x+y, x],[ x+y, x, y]|

Prove that abs[[1,x,x^2],[1,y,y^2],[1,z,z^2]]=(x-y)(y-z)(z-x)

Without expanding prove that abs[[x+y,y+z,z+x],[z,x,y],[1,1,1]]=0

If A(x_1, y_1), B(x_2, y_2) and C(x_3, y_3) are vertices of an equilateral triangle whose each side is equal to 'a', then prove that, |[x_1, y_1, 2 ],[ x_2, y_2, 2],[ x_3, y_3, 2]|^2=3 a^4

Find x and y if 2[[1,3],[0,x]]+[[y,0],[1,2]]=[[5,6],[1,8]]

Prove that |(1,x,x^3),(1,y,y^3),(1,z,z^3)|=(x+y+z)(x-y)(y-z)(z-y) .

If X-Y = [(1,1,1),(1,1,0),(1,0,0)] and X+Y = [(3,5,1),(-1,1,4),(11,8,0)] find X and Y ?

Find x, y, z and w if [[x-y, 2x+z],[2x-y, 3z+w]]=[[-1,5],[0,13]]

Find x and y satisfying the matrix equation [(x-y,2,-2),(4,x,6)] + [(3,-2,2),(1,0,-1)] = [(6,0,0),(5,2x+y,5)]

Draw the graph of 5x+10y=50,x+y=1,y=4,x,y=0.

V PUBLICATION-DETERMINANT-QUESTION BANK
  1. Let A=[[1,-2,1],[-2,3,1],[1,1,5]] verify that (A^(-1))^(-1)=A

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  2. Evaluate |[x, y, x+y],[ y, x+y, x],[ x+y, x, y]|

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  3. evaluate | [1,x,y],[1,x+y,y],[1,x,x+y] |

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  4. Using properties of determinants, prove that |[alpha, alpha^2, beta+g...

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  5. Using properties of determinants, prove that |[3a,-a+b,-a+c],[-b+a,3...

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  6. Using properties of determinants, prove that |[1,1+p,1+p+q],[2,3+2p,...

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  7. Using properties of determinants, prove that |[sinalpha,cosalpha,cos...

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  8. Consider a system of linear equations which is given below, 2/x+3/...

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  9. If a,b,c are in A.P., then the determinant |[x+2, x+3, x+2a],[x+3,x+...

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  10. If x, y, z are non zero real numbers, then find the inverse of matrix ...

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  11. Let A = [[1,Sintheta,1],[-Sintheta,1,Sintheta],[-1,-Sintheta,1]], wher...

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  12. If A(x1, y1), B(x2, y2) and C(x3, y3) are vertices of an equilateral t...

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  13. Solve the following system of equations using matrix method. 2 x+5 y=1...

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  14. If [[2,5],[-3,7]]xxA=[[17,-1],[47,-13]] then Find the 2x2 matrix A.

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  15. Let A=[[1 , 4, 0],[ -1, 2, 2],[ 0, 0, 2]] i) is A singular? i...

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  16. Solve the following system of equations using matrix method. 2 x+5 y=1...

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  17. Find the minors and cofactors of a(11), a(1 2) and a(13) of the matrix...

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  18. Let |A|=|[x1, x2, x3],[ y1, y2, y3],[ z1 , z2, z3]|.Expand |A| ...

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  19. Evaluate the determinant of A=[[3, -1, 2],[ 1, 2, -1],[ 4, 0, ...

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  20. Evaluate the determinant |[27, 2, 3],[ 45, 5, 5],[ 36, 9, 4]|

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