Advertisements
Advertisements
प्रश्न
Find the inverse of `[(1,2,3),(1,1,5),(2,4,7)]` by using elementary row transformations.
Advertisements
उत्तर
Let A = `[(1,2,3),(1,1,5),(2,4,7)]`
|A| = `|(1,2,3),(1,1,5),(2,4,7)|`
= 1(7 - 20) - 2(7 - 10) + 3(4 - 2)
= - 13 + 6 + 6
= - 1 ≠ 0
∴ A-1 exists.
Consider AA-1 = I
∴ `[(1,2,3),(1,1,5),(2,4,7)] "A"^-1= [(1,0,0),(0,1,0),(0,0,1)]`
By `"R"_2 - "R"_1 "and" "R"_3 - 2"R"_1` , we get,
`[(1,2,3),(0,-1,2),(0,0,1)] "A"^-1= [(1,0,0),(-1,1,0),(-2,0,1)]`
By `(- 1)"R"_2`we get
`[(1,2,3),(0,1,-2),(0,0,1)] "A"^-1 = [(1,0,0),(1,-1,0),(-2,0,1)]`
By `"R"_1 - 2"R"_2`we get
`[(1,0,7),(0,1,-2),(0,0,1)] "A"^-1 = [(-1,2,0),(1,-1,0),(-2,0,1)]`
By `"R"_1 - 7"R"_3` and `"R"_2 + 2"R"_3` we get
`[(1,0,0),(0,1,0),(0,0,1)] "A"^-1 = [(13,2,-7),(-3,-1,2),(-2,0,1)]`
∴ A-1 = `[(13,2,-7),(-3,-1,2),(-2,0,1)]`
APPEARS IN
संबंधित प्रश्न
Apply the given elementary transformation of the following matrix.
A = `[(5,4),(1,3)]`, C1↔ C2; B = `[(3,1),(4,5)]` R1↔ R2.
What do you observe?
Apply the given elementary transformation of the following matrix.
A = `[(1,2,-1),(0,1,3)]`, 2C2
B = `[(1,0,2),(2,4,5)]`, −3R1
Find the addition of the two new matrices.
Apply the given elementary transformation of the following matrix.
A = `[(1,-1,3),(2,1,0),(3,3,1)]`, 3R3 and then C3 + 2C2
Apply the given elementary transformation of the following matrix.
Use suitable transformation on `[(1,2),(3,4)]` to convert it into an upper triangular matrix.
Apply the given elementary transformation of the following matrix.
Convert `[(1,-1),(2,3)]` into an identity matrix by suitable row transformations.
Apply the given elementary transformation of the following matrix.
Transform `[(1,-1,2),(2,1,3),(3,2,4)]` into an upper triangular matrix by suitable column 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 = `((1,0,0),(2,1,0),(3,3,1))`, then reduce it to I3 by using column transformations.
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:
`((1,1),(1,1))`
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))`
Find the inverse of A = `[("cos" theta, -"sin" theta, 0),("sin" theta, "cos" theta, 0),(0,0,1)]` by elementary row transformations.
Find the inverse of A = `[("cos" theta, -"sin" theta, 0),("sin" theta, "cos" theta, 0),(0,0,1)]` by elementary column transformations.
If A = `[(2,3),(1,2)]`, B = `[(1,0),(3,1)]`, find AB and (AB)-1 . Verify that (AB)-1 = B-1.A-1.
If A = `[(4,5),(2,1)]`, show that `"A"^-1 = 1/6("A" - 5"I")`.
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)]`
If A = `[(1,0,1),(0,2,3),(1,2,1)]` and B = `[(1,2,3),(1,1,5),(2,4,7)]`, then find a matrix X such that XA = B.
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:
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
If A = `[(-2, 4),(-1, 2)]` then find A2
Find A−1 using column transformations:
A = `[(5, 3),(3, -2)]`
Find A−1 using column transformations:
A = `[(2, -3),(-1, 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)]`
Find the inverse of A = `[(2, -3, 3),(2, 2, 3),(3, -2, 2)]` by using elementary row transformations.
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)]`.
