Describe the possible echelon forms of the matrix. Use the notation of Example 1, A is a
Question:
Describe the possible echelon forms of the matrix. Use the notation of Example 1,
A is a 4 x 3 matrix, A = [a₁ a₂ a3], such that {a₁, a2} is linearly independent and a3 is not in Span {a₁, a₂}.
Transcribed Image Text:
- [₁ - EXAMPLE 1 Let A = 1-3 3 5 - - - - - - [ ] -- [] · u= 3 = 2 -5 2 and 5 3 -1 7 define a transformation T: R² → R³ by T(x) = Ax, so that 1-3 X1 = -DE X2 7 T(x) = Ax= 3 5 x13x2 3x1 + 5x₂ -X1 + 7x₂
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The columns must be linearly independent by Theorem 7 bec...View the full answer
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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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