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
`((5, 6),(7, 8))`
Find the rank of the following matrices
`((1, 4),(2, 8))`
Find the rank of the following matrices
`((1, 2, -1, 3),(2, 4, 1, -2),(3, 6, 3, -7))`
Solve the following system of equations by rank method
x + y + z = 9, 2x + 5y + 7z = 52, 2x – y – z = 0
Show that the equations 5x + 3y + 7z = 4, 3x + 26y + 2z = 9, 7x + 2y + 10z = 5 are consistent and solve them by rank method
The price of three commodities, X, Y and Z are and z respectively Mr. Anand purchases 6 units of Z and sells 2 units of X and 3 units of Y. Mr.Amar purchases a unit of Y and sells 3 units of X and 2 units of Z. Mr. Amit purchases a unit of X and sells 3 units of Y and a unit of Z. In the process they earn ₹ 5,000/-, ₹ 2,000/- and ₹ 5,500/- respectively. Find the prices per unit of three commodities by rank method
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
Find the rank of the matrix
A = `((1, -3, 4, 7),(9, 1, 2, 0))`
Examine the consistency of the system of equations:
x + y + z = 7, x + 2y + 3z = 18, y + 2z = 6
Find k if the equations 2x + 3y – z = 5, 3x – y + 4z = 2, x + 7y – 6z = k are consistent
