Concept explainers
Consider the
(a) Show that
(b) Why must
(c) What is the dimension of Span
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Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))
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- In Exercises 7-10, show that the given vectors form an orthogonal basis for2or3. Then use Theorem 5.2 to express was a linear combination of these basis vectors. Give the coordinate vector[w] ofwwith respect to the basis ={v1,v2}of 2or =v1,v2,v3 of3. v1=[111],v2=[110],v3=[112];w=[123]arrow_forwardComplete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner product p,q=a0b0+a1b1+a2b2+a3b3. An Orthonormal basis for P3. In P3, with the inner product p,q=a0b0+a1b1+a2b2+a3b3 The standard basis B={1,x,x2,x3} is orthonormal. The verification of this is left as an exercise See Exercise 17..arrow_forward
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