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Question
Find the rank of the matrix
A = `((-2, 1, 3, 4),(0, 1, 1, 2),(1, 3, 4, 7))`
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
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