Question

Asked Dec 27, 2019

14 views

Let S = {u1, u2, . . . , un} be a finite set of vectors. Prove that S is linearly dependent if and only if u1 = 0 or uk+1 ∈ span({u1, u2, . . . , uk}) for some k (1≤ k <n).

Step 1

Given:

Step 2

Since *S* is linearly dependent So:

Step 3

Now suppose,

...Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: A veterinarian depreciates a $10,000 X-ray machine. He estimates that the resale value V(t) (in $) a...

A: Click to see the answer

Q: The function to be optimized in a linear programming application is called the __________ function.

A: The function to be optimized in a linear programming application is called the objective function.

Q: For Exercise, a. Identify the center of the ellipse. b.Determine the value of a c.Determine the valu...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: For Exercise, determine the standard form of an equation of the parabola subject to the given condit...

A: Plot the given points line joining focus and vertex is parallel to y axis. That means axis is parall...

Q: For Exercise, write an inequality to represent the statement. y is at least −2

A: From the given information it is required to write the inequality for the given statement:Y is at le...

Q: Prove that W1 = {(a1, a2, . . . , an) ∈ Fn: a1 + a2 + · · · + an= 0} is a subspace of Fn , but W2 = ...

A: Prove that W1 = {(a1, a2, . . . , an) ∈ Fn: a1 + a2 + · · · + an= 0} is a subspace of Fn , but W2 = ...

Q: For Exercise, graph the equation. y = x2 + 4x + 3

A: Consider the given equation.

Q: One antifreeze solution is 36% alcohol and another is 20% alcohol. How much of each mixture should b...

A: It is given that, one antifreeze solution is 36% alcohol and another is 20% alcohol. Obtain the numb...

Q: a. Show that the points (2, 9), (−1, −6), and (−4, −3) are not collinear by finding the slope betwee...

A: a) Use the slope formula to find the slope between (2, 9) and (−1, −6)