please send handwritten solution for Q 7 part b 7. Let ū = (3,1,5), ở = (-1,1, 1), w = (3,0, 3).(a) Determine whether u can be written as a linear combination of ū and w. If possible, determinethe coefficients of the linear combination. Otherwise, state “NOT POSSIBLE".(b) Based on your answer in part (a), can {ữ, ū, w} span R³? Explain your reasoning.

Given that u=(3,1,5) , v =(-1,1,1) and w= (3,0,3)

7. Let ū = (3, 1,5), ở = (-1,1, 1), w = (3,0, 3). (a) Determine whether u can be written as a linear combination of i and w. If possible, determine the coefficients of the linear combination. Otherwise, state "NOT POSSIBLE". (b) Based on your answer in part (a), can {ữ, ī, w} span R³? Explain your reasoning.

7. Let ū = (3, 1,5), ở = (-1,1, 1), w = (3,0, 3). (a) Determine whether u can be written as a linear combination of i and w. If possible, determine the coefficients of the linear combination. Otherwise, state "NOT POSSIBLE". (b) Based on your answer in part (a), can {ữ, ī, w} span R³? Explain your reasoning.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 25EQ: Use the method of Example 2.23 and Theorem 2.6 to determine if the sets of vectors in Exercises...

See similar textbooks

Similar questions

Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)
Prove that if A is similar to B and A is diagonalizable, then B is diagonalizable.
Use the method of Example 2.23 and Theorem 2.6 to determine if the sets of vectors in Exercises 22-31 are linearly independent. If, for any of these, the answer can be determined by inspection (i.e., without calculation), state why. For any sets that are linearly dependent, find a dependence relationship among the vectors. [012],[213],[201]
1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2