Advertisements
Advertisements
प्रश्न
Show with the usual notation that for any matrix A = `["a"_"ij"]_(3xx3) "is" "a"_11"A"_11 + "a"_12"A"_12 + "a"_13"A"_13 = |"A"|`
Advertisements
उत्तर
A = `["a"_"ij"]_(3xx3) = [("a"_11,"a"_12,"a"_13),("a"_21,"a"_22,"a"_23),("a"_31,"a"_32,"a"_33)]`
`"A"_11 = (-1)^(1+1)"M"_11 = |("a"_22,"a"_23),("a"_32,"a"_33)|`
`"A"_12 = (-1)^(1+2)"M"_12 = - |("a"_21,"a"_23),("a"_31,"a"_33)|`
`"A"_13 = (-1)^(1+3)"M"_13 = |("a"_21,"a"_22),("a"_31,"a"_32)|`
∴ `"a"_11"A"_11 + "a"_12"A"_12 + "a"_13"A"_13`
`= "a"_11|("a"_22,"a"_23),("a"_32,"a"_33)| - "a"_12|("a"_21,"a"_23),("a"_31,"a"_33)| + "a"_13|("a"_21,"a"_22),("a"_31,"a"_32)|`
`= |("a"_11,"a"_12,"a"_13),("a"_21,"a"_22,"a"_23),("a"_31,"a"_32,"a"_33)| = |"A"|`
APPEARS IN
संबंधित प्रश्न
Apply the given elementary transformation of the following matrix.
A = `[(1,0),(-1,3)]`, R1↔ R2
Apply the given elementary transformation of the following matrix.
B = `[(1, -1, 3),(2, 5, 4)]`, R1→ R1 – R2
Apply the given elementary transformation of the following matrix.
Convert `[(1,-1),(2,3)]` into an identity matrix by suitable row transformations.
The total cost of 3 T.V. sets and 2 V.C.R.’s is ₹ 35,000. The shopkeeper wants a profit of ₹ 1000 per T.V. set and ₹ 500 per V.C.R. He sells 2 T.V. sets and 1 V.C.R. and gets the total revenue as ₹ 21,500. Find the cost price and the selling price of a T.V. set and a V.C.R.
If A = `[(2,1,3),(1,0,1),(1,1,1)]`, then reduce it to I3 by using row transformations.
Check whether the following matrix is invertible or not:
`[(1,0),(0,1)]`
Check whether the following matrix is invertible or not:
`((1,1),(1,1))`
Check whether the following matrix is invertible or not:
`((1,2),(3,3))`
Check whether the following matrix is invertible or not:
`((2,3),(10,15))`
Check whether the following matrix is invertible or not:
`(("sec" theta , "tan" theta),("tan" theta,"sec" theta))`
Check whether the following matrix is invertible or not:
`[(3,4,3),(1,1,0),(1,4,5)]`
Check whether the following matrix is invertible or not:
`((1,2,3),(2,-1,3),(1,2,3))`
Check whether the following matrix is invertible or not:
`((1,2,3),(3,4,5),(4,6,8))`
If A = `[("x",0,0),(0,"y",0),(0,0,"z")]` is a non-singular matrix, then find A−1 by using elementary row transformations. Hence, find the inverse of `[(2,0,0),(0,1,0),(0,0,-1)]`
Find the matrix X such that AX = B, where A = `[(1,2),(-1,3)]` and B = `[(0,1),(2,4)]`
Find X, if AX = B, where A = `[(1,2,3),(-1,1,2),(1,2,4)]` and B = `[(1),(2),(3)]`
Find A-1 by the adjoint method and by elementary transformations, if A = `[(1,2,3),(-1,1,2),(1,2,4)]`
Find the inverse of A = `[(1,0,1),(0,2,3),(1,2,1)]` by using elementary column transformations.
Find the inverse of `[(1,2,3),(1,1,5),(2,4,7)]` by using elementary row transformations.
Show with the usual notation that for any matrix A = `["a"_"ij"]_(3xx3) "is" "a"_11"A"_21 + "a"_12"A"_22 + "a"_13"A"_23 = 0`
Find the inverse of the following matrix (if they exist).
`[(1,3,-2),(-3,0,-5),(2,5,0)]`
Choose the correct answer from the given alternatives in the following question:
If A = `[(1,2),(3,4)]` , adj A = `[(4,"a"),(-3,"b")]`, then the values of a and b are
Choose the correct answer from the given alternatives in the following question:
The inverse of `[(0,1),(1,0)]` is
Choose the correct answer from the given alternatives in the following question:
If A = `[(1,2),(2,1)]` and A(adj A) = k I, then the value of k is
The element of second row and third column in the inverse of `[(1, 2, 1),(2, 1, 0),(-1, 0, 1)]` is ______.
If A = `[(2, -1, 1),(-2, 3, -2),(-4, 4, -3)]` the find A2
Find A−1 using column transformations:
A = `[(5, 3),(3, -2)]`
If A = `[(1, 2, -1),(3, -2, 5)]`, apply R1 ↔ R2 and then C1 → C1 + 2C3 on A
Find the matrix X such that `[(1, 2, 3),(2, 3, 2),(1, 2, 2)]` X = `[(2, 2, -5),(-2, -1, 4),(1, 0, -1)]`
If A = `[(2, 3),(1, 2)]`, B = `[(1, 0),(3, 1)]`, find AB and (AB)−1
If A = `[(cosθ, -sinθ, 0),(sinθ, cosθ, 0),(0, 0, 1)]`, find A–1
Find the matrix X such that AX = B, where A = `[(2, 1),(-1, 3)]`, B = `[(12, -1),(1, 4)]`.
