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If A=[(2,3),(1,-4)]and B=[(1,-2),(-1, 3)...

If `A=[(2,3),(1,-4)]`and `B=[(1,-2),(-1, 3)]`, then verify that `(A B)^(-1)=B^(-1)A^(-1)`

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To verify that \((AB)^{-1} = B^{-1}A^{-1}\) for the given matrices \(A\) and \(B\), we will follow these steps: ### Step 1: Define the matrices Let: \[ A = \begin{pmatrix} 2 & 3 \\ 1 & -4 \end{pmatrix}, \quad B = \begin{pmatrix} 1 & -2 \\ -1 & 3 \end{pmatrix} \] ...
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If A=[[2,-1,2],[1,3,-4]],B=[[1,-2],[-3,0],[5,4]] then verify that (AB)^(T)=B^(T)A^(T)

If A=[(2,1),(1,0)],B=[(1,-1),(2,3)] , verify that : (A+B)^(2)!=A^(2)+2AB+B^(2)

if A'=[{:(3,4),(-1,2),(0,1):}]and B=[{:(-1,2,1),(1,2,3):}], then verify that (i) (A+B)'=A'+B'(ii) (A-B)'=A'-B'

If A=[[1,3],[2,4]] and B=[[2,-1],[3,2]], verify that (AB)^(T)=B^(T)A^(T)

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NCERT-DETERMINANTS-SOLVED EXAMPLES
  1. Find the area of the triangle whose vertices are (3, 8),(-4, 2)and (5,...

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  2. Prove that |b+c a a b c+a b cc a+b|=4a b c

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  3. If x, y, z are different and Delta=|[x,x^2, 1+x^3],[y, y^2,1+y^3],[z, ...

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  4. Find the equation of the line joining A( 1,3) and B (0,0) using deter...

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  5. Find the minor of element 6 in the determinant Delta=|[1, 2, 3],[ 4, 5...

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  6. The sum of three numbers is 6. If we multiply third number by 3 and a...

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  7. Solve the following system of equations by matrix method. 3x-2y + 3z=...

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  8. Solve the system of equations 2x + 5y = 1 and 3x + 2y = 7.

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  9. Show that the matrix A=[[2,3],[ 1,2]]satisfies the equation A^2-4A+I=...

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  10. If A=[(2,3),(1,-4)]and B=[(1,-2),(-1, 3)], then verify that (A B)^(-1)...

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  11. If A=[[1 ,3 ,3],[ 1, 4 ,3],[ 1, 3, 4]],then verify thatA a d j A = |A|...

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  12. Find adj for A=[[1 ,2],[ 3 ,4]]

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  13. Find minors and cofactors of the elements of the determinant|[2,-3, 5...

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  14. Find minors and cofactors of the elements a(11), a(21) in the determi...

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  15. Find minors and cofactors of all the elements of the determinant |[1,...

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  16. If a, b, c are positive and unequal, show that value of the determina...

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  17. If a,b,c are in A.P, find value of |[2y+4,5y+7,8y+a],[3y+5,6y+8,9y+b],...

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  18. Show that Delta=|((y+z)^2,xy,zx),(xy,(x+z)^2,yz),(xz,yz,(x+y)^2)|=2xyz...

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  19. Use product [1-1 2 0 2-3 3-2 4][-2 0 1 9 2-3 6 1-2]to solve the syste...

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  20. Prove that Delta=|[a+bx, c+dx, p+qx],[ax+b, cx+d, px+q],[u ,v, w]|=(1-...

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