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Question
On using elementary column operations C2 → C2 – 2C1 in the following matrix equation `[(1, -3),(2, 4)] = [(1, -1),(0, 1)] [(3, 1),(2, 4)]`, we have: ______.
Options
`[(1, -5),(0, 4)] = [(1, -5),(-2, 2)] [(3, -5),(2, 0)]`
`[(1, -5),(0, 4)] = [(1, -1),(0, 1)] [(3, -5),(-0, 2)]`
`[(1, -5),(2, 0)] = [(1, -3),(0, 1)] [(3, 1),(-2, 4)]`
`[(1, -5),(2, 0)] = [(1, -1),(0, 1)] [(3, -5),(2, 0)]`
Solution
On using elementary column operations C2 → C2 – 2C1 in the following matrix equation `[(1, -3),(2, 4)] = [(1, -1),(0, 1)] [(3, 1),(2, 4)]`, we have: `[(1, -5),(2, 0)] = [(1, -1),(0, 1)] [(3, -5),(2, 0)]`.
Explanation:
Given that, `[(1, -3),(2, 4)] = [(1, -1),(0, 1)] [(3, 1),(2, 4)]`
Using C2 → C2 – 2C1, we get
`[(1, -5),(2, 0)] = [(1, -1),(0, 1)] [(3, -5),(2, 0)]`
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