3-1- 3-8-7Let P =- 3 - 4V1 =4,V2 =6 , and v3 =3Complete parts (a) and (b).14a. Find a basis (u,, u2, uz for R3 such that P is the change-of-coordinates matrix from fu,, u2, uz) to the basis (v1, v2, v3). [Hint: What do the columns of PC+Brepresent?]u, =,u, =uz =b. Find a basis (w,, W2, Wa) for R° such that P is the change-of-coordinates matrix from (v,, v2, V3 to (w,, w2, w3}.w, =W, =W2 =

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-1 -3 -8 -7 Let P = - 3 - 4 V1 = 4 ,V2 = 6 , and v3 = 3 Complete parts (a) and (b). 1 4 a. Find a basis fu,, u2, uz) for R such that P is the change-of-coordinates matrix from fu,, u2, uz) to the basis (v,, v2, v3). [Hint: What do the columns of P C- B represent?] u, = ,u, = uz = b. Find a basis (w,, w2, W3} for R° such that P is the change-of-coordinates matrix from {v,, v2, V3} to (w1, w2, w3}. w, = W, = W2 =

-1 -3 -8 -7 Let P = - 3 - 4 V1 = 4 ,V2 = 6 , and v3 = 3 Complete parts (a) and (b). 1 4 a. Find a basis fu,, u2, uz) for R such that P is the change-of-coordinates matrix from fu,, u2, uz) to the basis (v,, v2, v3). [Hint: What do the columns of P C- B represent?] u, = ,u, = uz = b. Find a basis (w,, w2, W3} for R° such that P is the change-of-coordinates matrix from {v,, v2, V3} to (w1, w2, w3}. w, = W, = W2 =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

3
-1
- 3
-8
-7
Let P =
- 3 - 4
V1 =
4
,V2 =
6 , and v3 =
3
Complete parts (a) and (b).
1
4
a. Find a basis (u,, u2, uz for R3 such that P is the change-of-coordinates matrix from fu,, u2, uz) to the basis (v1, v2, v3). [Hint: What do the columns of P
C+B
represent?]
u, =
,u, =
uz =
b. Find a basis (w,, W2, Wa) for R° such that P is the change-of-coordinates matrix from (v,, v2, V3 to (w,, w2, w3}.
w, =
W, =
W2 =

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