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3. When we refer to "The vector spaces" Rn (of column vectors), or Mnxm(R) (n x m matrices), or Pn (R) (polynomials of degree at most n), we mean those sets with their usual operations of vector addition and scalar multiplication (not, for example, the "re-defined" operation used above or any other operations). Use the subspace criterion to determine which of the following set are subspaces of these familiar vector spaces. (a) a S₁ = -{(i) = x²|0+h+c=0} = с (i.e. is S₁ a subspace of R³ under its usual operations of vector addition and scalar multiplication?)

3. When we refer to "The vector spaces" Rn (of column vectors), or Mnxm(R) (n x m matrices), or Pn (R) (polynomials of degree at most n), we mean those sets with their usual operations of vector addition and scalar multiplication (not, for example, the "re-defined" operation used above or any other operations). Use the subspace criterion to determine which of the following set are subspaces of these familiar vector spaces. (a) a S₁ = -{(i) = x²|0+h+c=0} = с (i.e. is S₁ a subspace of R³ under its usual operations of vector addition and scalar multiplication?)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. When we refer to "The vector spaces" R" (of column vectors), or Mnxm(R) (n x m matrices), or Pn (R) (polynomials of degree at most n), we mean those sets with their usual operations of vector addition and scalar multiplication (not, for example, the “re-defined" operation used above or any other operations). Use the subspace criterion to determine which of the following set are subspaces of these familiar vector spaces. (a) a ·- {(1) = (i.e. is S₁ a subspace of R³ under its usual operations of vector addition and scalar multiplication?) S₁ ER³|a+b+c=0
Transcribed Image Text:3. When we refer to "The vector spaces" R" (of column vectors), or Mnxm(R) (n x m matrices), or Pn (R) (polynomials of degree at most n), we mean those sets with their usual operations of vector addition and scalar multiplication (not, for example, the “re-defined" operation used above or any other operations). Use the subspace criterion to determine which of the following set are subspaces of these familiar vector spaces. (a) a ·- {(1) = (i.e. is S₁ a subspace of R³ under its usual operations of vector addition and scalar multiplication?) S₁ ER³|a+b+c=0
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