(a) Let I3 denote the 3 x 3 identity matrix. What should be the shape of in order for I3 to be computable? (b) I3 contains 3 column vectors e₁,e2, e3. Let x be a 3-vector [x1 2. Rewrite x in the form of a linear combination of e₁, €2, €3. (c) Part b tells us that I3 is a basis for R³ because any 3-vector can be written as a linear combination of the column vectors of I3. 1 However, I is not the only basis of R3. Prove that B = 0 0 linearly independent. 0 1 1 1 1 0 is a basis for R3 by showing that the columns of B are
(a) Let I3 denote the 3 x 3 identity matrix. What should be the shape of in order for I3 to be computable? (b) I3 contains 3 column vectors e₁,e2, e3. Let x be a 3-vector [x1 2. Rewrite x in the form of a linear combination of e₁, €2, €3. (c) Part b tells us that I3 is a basis for R³ because any 3-vector can be written as a linear combination of the column vectors of I3. 1 However, I is not the only basis of R3. Prove that B = 0 0 linearly independent. 0 1 1 1 1 0 is a basis for R3 by showing that the columns of B are
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
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