Question: Let v denote a vector in an inner product space V. (a) Show that W = (w | w in V,(v, w) = 0} is

Let v denote a vector in an inner product space V.
(a) Show that W = (w | w in V,(v, w) = 0} is a subspace of V.
(b) If V= R3 with the dot product, and if v = (1, -1, 2), find a basis for IV.

Step by Step Solution

★★★★★

3.42 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

b 26b Here W w w in R 3 and v w 0 x y z x y 2z ... 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)

950-M-L-A-L-S (6692).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let u be a vector in an inner product space V, and let (v1, v2, ..., vn) be an orthonormal basis for V. Show that if a1 is the angle between u and vi then Cos2a1 + cos22 + . . . + cos2an = 1

Let v be a vector in an inner product space V. (a) Show that ||v|| > ||projU(v)|| holds for all finite dimensional subspaces U. [Hint: Pythagoras' theorem.] If {e1,e2,..., ew} is any orthogonal set...

Let v0 be a fixed vector in an inner product space V, and let T: V V be defined by T(v) = (v, v0)v0. Show that T is a linear operator on V.

3 10 marks Let V P 1 1 be a inner product space with inner product defined by f t g t dt for f 9 V Find the polynomial of degree one or less in V that is closest to h x sin x in V

Let V denote the vector space C [-1, l] of continuous real-valued functions on the closed interval [- 1, 1]. So, for example, the functions ET and cos(z) :r:2 belong to this vector space (where both...

rch Q1 1 Point If A is a singular n X n matrix, then the associated homogeneous system represented by An? = 6 has only the trivial solution. 0 True 0 False Q2 1 Point Let V denote the vector space of...

Let W be a subspace of an inner product space V and let {w1, w2, ... wm} be an orthogonal basis for W. Show that if v is any vector in V, then (v, wi) (v, w2) (V, W res

(5 points) Let V be a vector space over some field F (a) (3 points) Let W be a subspace of a vector space V. Suppose x, y V are not in W. Show that if re span (W,y) then y = span (W, x) b) (2 point)...

2. (4+4+2) Let V denote the vector space of all third-degree or less polynomials. We consider two bases for V, B1 = {1, x, x2, x3 } B2 = {1, x - 1, (x - 1)(x - 2), (x -1)(x -2)(x -3)} (a) Find the...

Q1 1 Point Determine if the following statement is True or False. The following set of vectors from P2 (the set of all polynomials of degree :1 2): {p1(t) = t2 + 5t + 6,11)2(2):t2 + 525 + 4} form a...

Two football teams play against each other. The offense can choose to pass or run, and the defense can choose to defend against either the pass or run. Depending on the combination of choices, the...

Consider the x and R chart that you established in Exercise 6.15 for the piston ring process. Suppose that you want to continue control charting piston ring diameter using n = 3. What limits would be...

On 1st January, 2016 Sadhan Sen of Sodepur sent 1,000 units of silk goods to Biren Bose of Berhampur .The goods cost ~ 75,000 to Sadhan and these were sent on consignment basis. Sadhan had to incur...

The four most important limitations on the powerof federal agencies are statutory control in the enabling legislation and the APA; poli tical control by Congress and the president; judicial review;...

A person who is exercising should not exceed his or her maximum heart rate, which is determined on the basis of that person's sex, age, and resting heart rate. The table below relates resting heart...

A math instructor asked her students to keep track of how much time each spent studying a chapter on functions in her algebra-trigonometry course. She collected the information together with test...

Find the slope of the line containing the given points. (a) (2, -8) and (-5, -1) (b) (5, 7) and (5, -7)

An urgent!, urgent! and urgent! Challenging University of Cumberland Case study A and statistics question. 2. Find the probability that a normal random variable X with mean m = 1,600 and standard...

6. (1.5 pt) Bob and Ann both make optimal portfolio allocations. Bob has $ 1000 to invest, Ann has $ 2000 to invest. There are 3 assets that they can invest in: a risk free asset with a rate of...

Kenneth secured a 4 - year car loan at 5 . 6 0 % compounded annually that required him to make payments of $ 8 8 2 . 8 1 at the beginning of each month. Calculate the cost of the car if he made a...