Advertisements
Advertisements
प्रश्न
Find the inverse of the following by Gauss-Jordan method:
`[(1, 2, 3),(2, 5, 3),(1, 0, 8)]`
उत्तर
A = `[(1, 2, 3),(2, 5, 3),(1, 0, 8)]`
`[A|I3] = `[(1, 2, 3, |, 1, 0, 0),(2, 5, 3, |, 0, 1, 0),(1, 0, 8, |, 0, 0, 1)]`
`{:("R"_2 -> "R"_ - 2"R"_1),("R"_3 -> "R"_3 - "R"_1),(->):} [(1, 2, 3, |, 1, 0, 0),(0, 1, -3, |, -2, 1, 0),(0, -2, -5, |, -1, 0, 1)]`
`{:("R"_3 -> "R"_3 + 2"R"_2),(->):} [(1, 2, 3, |, 1, 0, 0),(0, 1, -3, |, -2, 1, 0),(0, 0, -1, |, -5, 2, 1)]`
`{:("R"_2 -> (-) "R"_3),(->):} [(1, 2, 3, |, 1, 0, 0),(0, 1, -3, |, -2, 1, 0),(0, 0, 1, |, 5, -2, -1)]`
`{:("R"_2 -> "R"_2 + 3"R"_3),(->):} [(1, 2, 3, |, 1, 0, 0),(0, 1, -3, |, -2, 1, 0),(0, 0, 1, |, 5, -2, -1)]`
`{:("R"_2 -> "R"_2 + "R"_1),(->):} [(1, 2, 3, |, 1, 0, 0),(0, 1, 0, |, 13, -5, -3),(0, 0, 1, |, 5, -2, -1)]`
`{:("R"_1 -> "R"_1 - 2"R"_2),(->):} [(1, 0, 3, |, -25, 10, 6),(0, 1, 0, |, 13, -5, -3),(0, 0, 1, |, 5, -2, -1)]`
`{:("R"_1 -> "R"_1 - 3"R"_3),(->):} [(1, 0, 0, |, -40, 16, 9),(0, 1, 0, |, 13, -5, -3),(0, 0, 1, |, 5, -2, -1)]`
∴ `"A"^-1 = [(-40, 16, 9),(13, -5, -3),(5, -2, -1)]`
APPEARS IN
संबंधित प्रश्न
Find the rank of the following matrices by minor method:
`[(2, -4),(-1, 2)]`
Find the rank of the following matrices by minor method:
`[(-1, 3),(4, 7),(3, 4)]`
Find the rank of the following matrices by minor method:
`[(1, -2 - 1, 0),(3, -6 - 3, 1)]`
Find the rank of the following matrices by minor method:
`[(1, -2, 3),(2, 4, -6),(5, 1, -1)]`
Find the rank of the following matrices by minor method:
`[(0, 1 ,2, 1),(0, 2, 4, 3),(8, 1, 0, 2)]`
Find the rank of the following matrices by row reduction method:
`[(1, 2, -1),(3, -1, 2),(1, -2, 3),(1, -1, 1)]`
Find the rank of the following matrices by row reduction method:
`[(3, -8, 5, 2),(2, -5, 1, 4),(-1, 2, 3, -2)]`
Find the inverse of the following by Gauss-Jordan method:
`[(2, -1),(5, -2)]`
Find the inverse of the following by Gauss-Jordan method:
`[(1, -1, 0),(1, 0, -1),(6, -2, -3)]`
Choose the correct alternative:
If A = `[(3, 1, -1),(2, -2, 0),(1, 2, -1)]` and `"A"^-1 = [("a"_11, "a"_12, "a"_13),("a"_21, "a"_22, "a"_23),("a"_31, "a"_32, "a"_33)]` then the value of a23 is
Choose the correct alternative:
The rank of the matrix `[(1, 2, 3, 4),(2, 4, 6, 8),(-1, -2, -3, -4)]` is
Choose the correct alternative:
If xayb = em, xcyd = en, Δ1 = `|("m", "b"),("n", "d")|`, Δ2 = `|("a", "m"),("c", "n")|`, Δ3 = `|("a", "b"),("c", "d")|`, then the values of x and y are respectively,
Let A = {1, 3, 5} and B = {x : x is an odd natural number less than 6}. Then, which of the following are true?
