Advertisements
Advertisements
प्रश्न
Find the rank of the matrix
A = `((-2, 1, 3, 4),(0, 1, 1, 2),(1, 3, 4, 7))`
Advertisements
उत्तर
A = `[(-2, 1, 3, 4),(0, 1, 1, 2),(1, 3, 4, 7)]`
The order of A is 3 × 4
∴ P(A) < 3
Let us transform the matrix A to an echelon form
| Matrix | Elementary Transformation |
| A = `[(-2, 1, 3, 4),(0, 1, 1, 2),(1, 3, 4, 7)]` | |
| `∼ [(-2, 1, 3, 4),(1, 3, 4, 7),(0, 1, 1, 2)]` | `{:"R"_2 ↔ "R"_3:}` |
| `∼ [(1, 3, 4, 7),(-2, 1, 3, 4),(0, 1, 1, 2)]` | `{:"R"_2 ↔ "R"_1:}` |
| `∼ [(1, 3, 4, 7),(0, 7, 11, 18),(0, 1, 1, 2)]` | `{:"R"_2 -> "R"_2 + 2"R"_1:}` |
| `∼ [(1, 3, 4, 7),(0, 1, 1, 2),(0, 7, 11, 18)]` | `{:"R"_3 ↔ "R"_2:}` |
| `∼ [(1, 3, 4, 7),(0, 1, 1, 2),(0, 0, 4, 4)]` | `{:"R"_3 -> "R"_3 + 7"R"_2:}` |
The number of non-zero rows = 3
∴ p(A) = 3
APPEARS IN
संबंधित प्रश्न
Find the rank of the following matrices
`((1, 2, -1, 3),(2, 4, 1, -2),(3, 6, 3, -7))`
Find the rank of the following matrices
`((3, 1, -5, -1),(1, -2, 1, -5),(1, 5, -7, 2))`
If A = `((1, 1, -1),(2, -3, 4),(3, -2, 3))` and B = `((1, -2, 3),(-2, 4, -6),(5, 1, -1))`, then find the rank of AB and the rank of BA.
Show that the equations 5x + 3y + 7z = 4, 3x + 26y + 2z = 9, 7x + 2y + 10z = 5 are consistent and solve them by rank method
For what values of the parameter λ, will the following equations fail to have unique solution: 3x – y + λz = 1, 2x + y + z = 2, x + 2y – λz = – 1
Choose the correct alternative:
If A = `((2, 0),(0, 8))`, then p(A) is
Choose the correct alternative:
The rank of the diagonal matrix `[(1, , , , ,),(, 2, , , ,),(, , -3, , ,),(, , , 0, ,),(, , , , 0,),(, , , , ,0)]`
Choose the correct alternative:
Which of the following is not an elementary transformation?
Choose the correct alternative:
Rank of a null matrix is
Find the rank of the matrix
A = `((1, -3, 4, 7),(9, 1, 2, 0))`
