Advertisements
Advertisements
Question
If A = `[(1,1),(1,2)], "B" = [(4,1),(3,1)]` and C = `[(24,7),(31,9)]`, then find the matrix X such that AXB = C
Advertisements
Solution
Since, AXB = C
∴ `[(1,1),(1,2)] ("XB") = [(24,7),(31,9)]`
First we perform the row transformations.
Applying R2 → R2 − R1,
`[(1,1),(0,1)] ("XB") = [(24,7),(7,2)]`
Applying R2 → R1 − R2,
`[(1,0),(0,1)] ("XB") = [(17,5),(7,2)]`
∴ XB = `[(17,5),(7,2)]`
∴ X `[(4,1),(3,1)] = [(17,5),(7,2)]`
Now, we perform the column transformations.
Applying C1 ↔ C2,
`"X" [(1,4),(1,3)] = [(5,17),(2,7)]`
Applying C2 → C2 − 4C1,
`"X"[(1,0),(1,-1)] = [(5,-3),(2,-1)]`
Applying C2 → −C2,
`"X"[(1,0),(1,1)] = [(5,3),(2,1)]`
Applying C1 → C1 − C2,
`"X"[(1,0),(0,1)] = [(2,3),(1,1)]`
∴ X = `[(2,3),(1,1)]`
RELATED QUESTIONS
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.
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.
A = `[(1,-1,3),(2,1,0),(3,3,1)]`, 3R3 and then C3 + 2C2
and A = `[(1,-1,3),(2,1,0),(3,3,1)]`, C3 + 2C2 and then 3R3
What do you conclude?
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.
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:
`[(cos theta, sin theta),(-sin theta, cos theta)]`
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:
`((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)]`
If A = `[(1,2),(3,4)]` and X is a 2 × 2 matrix such that AX = I, find X.
Find the inverse of A = `[("cos" theta, -"sin" theta, 0),("sin" theta, "cos" theta, 0),(0,0,1)]` by elementary row 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 X, if AX = B, where A = `[(1,2,3),(-1,1,2),(1,2,4)]` and B = `[(1),(2),(3)]`
Find the inverse of A = `[(1,0,1),(0,2,3),(1,2,1)]` by using elementary column 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`
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"|`
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
If A = `[(2, -1, 1),(-2, 3, -2),(-4, 4, -3)]` the find A2
If A = `[(-2, 4),(-1, 2)]` then find A2
Find the matrix X such that AX = I where A = `[(6, 17),(1, 3)]`
Find A−1 using column transformations:
A = `[(2, -3),(-1, 2)]`
Find the inverse of A = `[(2, -3, 3),(2, 2, 3),(3, -2, 2)]` by using elementary row transformations.
If A = `[(3, -1),(4, 2)]`, B = `[(2),(-1)]`, find X such that AX = B.
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)]`.
