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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 19E

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determined whether or not the set of vector (1,7,2), (8,0,6), (1,6,4) to form a basis for R^3

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Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector space?
Find a basis for R2 that includes the vector (2,2).
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Do the vectors (1,1,3),(2,3,6) and (1,4,3) form a basis for R^3
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Does the ordered set v, v, va form a basis for R^3? If not, which vectors would you subtract from the set and which standard basis vector can you add to the set to make it a basis for R^3? vi = (1,–1, –2) = (5, –4, –7) v = (-3, 1,0) Select all answers that are correct. O subtract vector v 1 from the set O no it does not form a basis for R^3 O subtract vector v_3 from the set O yes it forms a basis for R^3 O add vector e_1 O add vector e 2 subtract vector v_2 from the set O add vector e_3
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3) Let C be a basis that contains vectors 2 (−2 + 1x + 1x^ + (−1) x3), (1 + (−2) x + 4x2 + 2x3), (−2 + 1x + 1x2 + (-1) 3), (−4 + 4x + 2 + 4x3) and P = C-B -1 Then : b₁ b2 = , b3 : = , ba = 3 = 4 4 -1 4 -24 -2 -2 2 ↓ NALN -1 -4 -2

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