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Problem 9. Let V1 = , V2 > V3 = 2 V4 = be vectors in R³. (i) Explain whyY you can deduce from Problem 8 that each of the two subsets, Вз {V1, V2, V3}, B4 {v1, V2, V4} forms a basis of R³. (ii) Find the transition matrix P such that |x]B, = P[x]B,. If (:). [y]B4 -2 B4 find [y]B3. Check your answers by using [y]B, and [y]B, to write y in standard coordinates.

Problem 9. Let V1 = , V2 > V3 = 2 V4 = be vectors in R³. (i) Explain whyY you can deduce from Problem 8 that each of the two subsets, Вз {V1, V2, V3}, B4 {v1, V2, V4} forms a basis of R³. (ii) Find the transition matrix P such that |x]B, = P[x]B,. If (:). [y]B4 -2 B4 find [y]B3. Check your answers by using [y]B, and [y]B, to write y in standard coordinates.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.1: Introduction To Systems Of Linear Equations
Problem 90E: Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the...
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(3) Problem 9. Please provide a typewritten solution, I will be very grateful!
Solve only PROBLEM 9. I attached here a pic of Problem 8 , because in the tasks in Problem 9 it is needed!

Problem 8. For a constant deR, consider the following system of linear equations x + 2y + z Зх + 5у + 22 = 1 Y + dz 2. (i) Find all values of A for which the syslem of equalions is consistent. If the system is consistent, is the solution unique? Justify your answer. (ii) In the case(s) that the above system has a unique solution, use Cramer's rule to find the value of z in terms of ).
Transcribed Image Text:Problem 8. For a constant deR, consider the following system of linear equations x + 2y + z Зх + 5у + 22 = 1 Y + dz 2. (i) Find all values of A for which the syslem of equalions is consistent. If the system is consistent, is the solution unique? Justify your answer. (ii) In the case(s) that the above system has a unique solution, use Cramer's rule to find the value of z in terms of ).
Problem 9. Let () 2 Vị V2 V3 V4 1 be vectors in R³. (i) Explain why you can deduce from Problem 8 that each of the two subsets, B3 = {V1, V2, V3}; B1 = {V1, V2, V4} forms a basis of R³. (ii) Find the transition matrix P such thal |x]7, = P|x]z,- Px|BA B3 If 3 -2 B4 4 B4 find y B3. Check your answers by using yB, and y B, to write y in standard coordinates.
Transcribed Image Text:Problem 9. Let () 2 Vị V2 V3 V4 1 be vectors in R³. (i) Explain why you can deduce from Problem 8 that each of the two subsets, B3 = {V1, V2, V3}; B1 = {V1, V2, V4} forms a basis of R³. (ii) Find the transition matrix P such thal |x]7, = P|x]z,- Px|BA B3 If 3 -2 B4 4 B4 find y B3. Check your answers by using yB, and y B, to write y in standard coordinates.
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