Question: Suppose that S = {v1, v2, v3} is a set of three vectors from C873. Prove that the set T = {2v1 + 3v2 +

Suppose that S = {v1, v2, v3} is a set of three vectors from C873. Prove that the set
T = {2v1 + 3v2 + v3, v1 - v2 - 2v3, 2v1 + v2 - v3}
is linearly dependent.

Step by Step Solution

★★★★★

3.50 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

By Definition LICV we can complete this problem by finding scalars 1 2 3 not all zer... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

961-M-L-A-L-S (5920).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Suppose that S = {v1, v2, v3} is a linearly independent set of three vectors from C873. Prove that the set T = {2v1 + 3v2 + v3, v1 - v2 + 2v3, 2v1 + v2 - v3} is linearly independent.

Suppose that S = {v1, v2, v3} is a linearly independent set of vectors in a vector space V. Prove that T = {w1, w2, w3} is also linearly independent, where w1 = v1 + v2 + v3, w2 = v2 + v3, and w3 =...

Suppose that S = [v1, v2, v3} is a linearly dependent set of vectors in a vector space V. Is T = {w1, w2, w3}, where w1 = v1, w2 = v1, + v3, w3 = v1, + v2 + v3, linearly dependent or linearly...

Let V be a vector space, and suppose v1, v2, v3 span V . If u1 = v1 + v2, u2 = v1 v2, u3 = 2v1 + 3v2 v3, show that u1, u2, u3 span V.

MAT 2 4 2 , Fall 2 0 2 4 Written Homework 4 Instructor: Oleksandr Lytvak 1 . ( 5 points ) Let B = { ~v 1 , ~v 2 , ~v 3 } be the set of vectors, where ~v 1 = 3 4 1 4 , ~v 2 = 5 2 3 k , ~v 3 = 2 m 2 8...

Suppose that {v1, v2, v3, ... , vn} is a set of vectors. Prove that {v1 - v2, v2 - v3, v3 - v4, ... , vn - v1} is a linearly dependent set.

All vectors and subspaces are in R". Check the true statements below: A. For each y and each subspace W, the vector y projw(y) is orthogonal to W. B. If z is orthogonal to u1 and u2 and if W =...

1. Describe how to construct a field of order 8 = 23 as a quotient ring R/I (i.e., state what the appropriate ring R and ideal I are). In particular, describe what the elements of the ring R/I are...

Math 308 B: Essay Homework #3 Due: Friday, May 1 in class Problem 1: (a) Suppose that T : Rm Rn is a linear transformation which is one-to-one and suppose that {v1 , v2 } is a linearly independent...

Suppose that {v1, v2, v3, v4} is a linearly independent set in C35. Prove that {v1, v1 + v2, v1 + v2 + v3, v1 + v2 + v3 + v4} is a linearly independent set.

Using a _________ is a way of omitting extraneous details from an economic model. a. critical assumption b. theory c. normative statement d. simplifying statement e. descriptive simplification

Gold Star Industries is contemplating a purchase of computers. The firm has narrowed its choices to the SAL 5000 and the HAL 1000. Gold Star would need 9 SALs, and each SAL costs $3,700 and requires...

15. Hayes Company purchased 10,000 ordinary shares of Kenyon Co., paying $26 per share plus $1,500 in broker fees. Hayes plans to actively trade this investment. Prepare the entry to record this...

5. The data below show a countrys national debt and its prime lending rate. a. Plot the relationship between national debt and the lending rate. b. Based on your graph, does crowding out appear to be...

Let V be an inner product space. Show that if u and v are orthogonal unit vectors in V, then ||u - v|| = 2.

Let V be an inner product space. Show that if w is orthogonal to each of the vectors u1,u2, ... ,ur, then it is orthogonal to every vector in span (u1, u2,..., ur,}.

Let {w1, w2,..., wk} be a basis for a subspace W of V. Show that W consists of all vectors in V that are orthogonal to every basis vector.

Tinbergen Cans expects sales next year to be $50,000,000. Inventory and accounts receivable (combined) will increase $8,000,000 to accommodate this sales level. The company has a profit margin of 6...

Java programming please help! What needs to go into > for the code to output: 2 3 4 for (int num =2;; num++) System.out. println(num); \} num>4 num==4 num

consider the following information tor three stocks, stock A, stock B, and Stock C. The returns on each of the three stocks are positively correlated, but they are not perfectly correlated. (That is,...