Consider the polynomials p₁ (t)=3-t³, p₂ (t)=2-t², p₂ (t)=t-5t², and p₁ (t)=7-t+3t² −1³. 3 Is {P₁, P2, P3, P4} a basis for P3? Why or why not? If not, write one vector as a linear combination of the others.
Consider the polynomials p₁ (t)=3-t³, p₂ (t)=2-t², p₂ (t)=t-5t², and p₁ (t)=7-t+3t² −1³. 3 Is {P₁, P2, P3, P4} a basis for P3? Why or why not? If not, write one vector as a linear combination of the others.
Consider the polynomials p₁ (t)=3-t³, p₂ (t)=2-t², p₂ (t)=t-5t², and p₁ (t)=7-t+3t² −1³. 3 Is {P₁, P2, P3, P4} a basis for P3? Why or why not? If not, write one vector as a linear combination of the others.
Is the set of vectors a basis for P3? If not, write one vector as a linear combination of the others.
Transcribed Image Text:Consider the polynomials p₁ (t) = 3−t³, p₂ (t) = 2−t², p3 (t)=t-5t², and p₁(t)=7−t+3t² −t³.
Is {P₁, P₂, P3, P4} a basis for P3? Why or why not? If not, write one vector as a linear
29
combination
of the others.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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