Represent vectors using basisMore details. (a) Let I3 denote the 3 x 3 identity matrix. What should be the shape of x in order for I3x to be computable?(b) I3 contains 3 column vectors €₁, €2, €3. Let x be a 3-vectorx1X2Rewrite x in the form of a linear combination of e1,e2, e3X3(c) Part b tells us that I is a basis for R³ because any 3-vector can be written as a linear combination of the column vectors of I3.However, I3 is not the only basis of R³. Prove that Blinearly independent.=011is a basis for R³ by showing that the columns of B are (d) Normally, the 3-vector we write down uses basis I3. For example, b=+3+621+228uses basis I3. Now express vector busing basis B. In other words, you are trying to find scaler 21, 22, 23 such that+23H.Finally, z =2122 is how you represent busing basis B.Z3

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(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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Represent vectors using basis

More details.

(a) Let I3 denote the 3 x 3 identity matrix. What should be the shape of x in order for I3x to be computable?
(b) I3 contains 3 column vectors €₁, €2, €3. Let x be a 3-vector
x1
X2
Rewrite x in the form of a linear combination of e1,e2, e3
X3
(c) Part b tells us that I is a basis for R³ because any 3-vector can be written as a linear combination of the column vectors of I3.
However, I3 is not the only basis of R³. Prove that B
linearly independent.
=
0
1
1
is a basis for R³ by showing that the columns of B are

(d) Normally, the 3-vector we write down uses basis I3. For example, b
=
+3
+6
21
+22
8
uses basis I3. Now express vector busing basis B. In other words, you are trying to find scaler 21, 22, 23 such that
+23
H.
Finally, z =
21
22 is how you represent busing basis B.
Z3

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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