Find the matrix P that transforms S₁ to S₂ for the following pairs of bases. 1. S₁ = {(2, 5), (1, 1)), S₂= {(1, 3), (0, 2)} 2. S₁= {(1, 0), (0, 1)), S₂ = {(a, b), (c, d)} 3. S₁ = {(a, b), (c, d)}, S₂ = {(1, 0), (0, 1)} 4. What conditions on a,b, c, and d make part (c) impossible? Why?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Find the matrix P that transforms S₁ to S₂ for the following pairs of bases.
1. S₁ = {(2, 5), (1, 1)), S₂ = {(1, 3), (0, 2)}
2. S₁ = {(1, 0), (0, 1)), S₂ = {(a, b), (c, d)}
3. S₁ = {(a, b), (c, d)}, S₂ = {(1, 0), (0, 1)}
4. What conditions on a,b, c, and d make part (c) impossible? Why?
Transcribed Image Text:Find the matrix P that transforms S₁ to S₂ for the following pairs of bases. 1. S₁ = {(2, 5), (1, 1)), S₂ = {(1, 3), (0, 2)} 2. S₁ = {(1, 0), (0, 1)), S₂ = {(a, b), (c, d)} 3. S₁ = {(a, b), (c, d)}, S₂ = {(1, 0), (0, 1)} 4. What conditions on a,b, c, and d make part (c) impossible? Why?
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