Problem 1. a. The set of solutions to the system of linear equation +2.r3 2.r1 +3r2 -24 = 0 +9x2 -6.r3 = 0 is a subspace of R'. Find a basis for and the dimension of this subspace. b. If T: P (R) → R* is a linear transformation such that T(1 + 2x) = (2, 3, 4) and T(x)= (1,2, –2), find T(2+7x). Is T one-to-one? Is T onto? CS Scanned with CamScanner

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Problem 1.
a. The set of solutions to the system of linear equation
+2.x3
= 0
2.r1
+3r2
-24
= 0
+9x2
-6.r3
2.aA
= 0
is a subspace of R'. Find a basis for and the dimension of this subspace.
b. If T : P;(R) → R is a linear transformation such that T(1 + 2x) = (2, 3, 4) and T(x)= (1,2, –2), find T(2 +7x). Is
T one-to-one? Is T onto?
CS
Scanned with CamScanner
Transcribed Image Text:Problem 1. a. The set of solutions to the system of linear equation +2.x3 = 0 2.r1 +3r2 -24 = 0 +9x2 -6.r3 2.aA = 0 is a subspace of R'. Find a basis for and the dimension of this subspace. b. If T : P;(R) → R is a linear transformation such that T(1 + 2x) = (2, 3, 4) and T(x)= (1,2, –2), find T(2 +7x). Is T one-to-one? Is T onto? CS Scanned with CamScanner
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