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
`((3, 1, -5, -1),(1, -2, 1, -5),(1, 5, -7, 2))`
Choose the correct alternative:
If p(A) = r then which of the following is correct?
Choose the correct alternative:
If A = `((1),(2),(3))` then the rank of AAT is
Choose the correct alternative:
If p(A) = p(A,B)= then the system is
Choose the correct alternative:
If p(A) ≠ p(A, B) =, then the system is
Choose the correct alternative:
For the system of equations x + 2y + 3z = 1, 2x + y + 3z = 3, 5x + 5y + 9z = 4
Choose the correct alternative:
If `|"A"_("n" xx "n")|` = 3 and |adj A| = 243 then the value n is
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 x + y + z = 1, 3x – y – z = 4, x + 5y + 5z = k are inconsistent
