Advertisements
Advertisements
Question
Find the rank of the matrix
A = `((-2, 1, 3, 4),(0, 1, 1, 2),(1, 3, 4, 7))`
Advertisements
Solution
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
RELATED QUESTIONS
Find the rank of the following matrices
`((1, -1),(3, -6))`
Find the rank of the following matrices
`((-1, 2, -2),(4, -3, 4),(-2, 4, -4))`
Choose the correct alternative:
If A = `((1),(2),(3))` then the rank of AAT 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:
If p(A) ≠ p(A, B) =, then the system is
Choose the correct alternative:
If the number of variables in a non-homogeneous system AX = B is n, then the system possesses a unique solution only when
Choose the correct alternative:
The system of equations 4x + 6y = 5, 6x + 9y = 7 has
Choose the correct alternative:
The system of linear equations x = y + z = 2, 2x + y – z = 3, 3x + 2y + k = 4 has unique solution, if k is not equal to
Find k if the equations x + y + z = 1, 3x – y – z = 4, x + 5y + 5z = k are inconsistent
