Question

2. (a) Determine if B = 1 0 1 1 , 1 0 −2 1 ,...

2. (a) Determine if B = 1 0 1 1 , 1 0 −2 1 , −2 0 7 −2 spans L2×2. (Here L2×2 denote vector space of all 2 × 2 lower triangular real matrices.)

(b) Check if S2 = x 2 + x + 1, 2x − 1, 3x 2 − 5 spans P2(x) (Here P2(x) is a vector space containing polynomials of degree less than or equal to 2.)

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let P2 denote the vector space of polynomials in x with real coefficients having degree at...
Let P2 denote the vector space of polynomials in x with real coefficients having degree at most 2. Let W be a subspace of P2 given by the span of {x2−x+6,−x2+2x−1,x+5}. Show that W is a proper subspace of P2.
1)T F: All (x, y, z) ∈ R 3 with x = y + z is...
1)T F: All (x, y, z) ∈ R 3 with x = y + z is a subspace of R 3 9 2) T F: All (x, y, z) ∈ R 3 with x + z = 2018 is a subspace of R 3 3) T F: All 2 × 2 symmetric matrices is a subspace of M22. (Here M22 is the vector space of all 2 × 2 matrices.) 4) T F: All polynomials of degree exactly 3 is...
If V is a vector space of polynomials of degree n with real numbers as coefficients,...
If V is a vector space of polynomials of degree n with real numbers as coefficients, over R, and W is generated by the polynomials (x 3 + 2x 2 − 2x + 1, x3 + 3x 2 − x + 4, 2x 3 + x 2 − 7x − 7), then is W a subspace of V , and if so, determine its basis.
We have learned that we can consider spaces of matrices, polynomials or functions as vector spaces....
We have learned that we can consider spaces of matrices, polynomials or functions as vector spaces. For the following examples, use the definition of subspace to determine whether the set in question is a subspace or not (for the given vector space), and why. 1. The set M1 of 2×2 matrices with real entries such that all entries of their diagonal are equal. That is, all 2 × 2 matrices of the form: A = a b c a 2....
Determine if the given set V is a subspace of the vector space W, where a)...
Determine if the given set V is a subspace of the vector space W, where a) V={polynomials of degree at most n with p(0)=0} and W= {polynomials of degree at most n} b) V={all diagonal n x n matrices with real entries} and W=all n x n matrices with real entries *Can you please show each step and little bit of an explanation on how you got the answer, struggling to learn this concept?*
3. Which of the following sets spans P2(R)? (a) {1 + x, 2 + 2x 2}...
3. Which of the following sets spans P2(R)? (a) {1 + x, 2 + 2x 2} (b) {2, 1 + x + x 2 , 3 + 2x + 2x 2} (c) {1 + x, 1 + x 2 , x + x 2 , 1 + x + x 2} 4. Consider the vector space W = {(a, b) ∈ R 2 | b > 0} with defined by (a, b) ⊕ (c, d) = (ad + bc, bd)...
Consider V = fp(t) 2 P2 : p0(1) = p(0)g, where P2 is a set of...
Consider V = fp(t) 2 P2 : p0(1) = p(0)g, where P2 is a set of all polynomials of degree less than or equal to 2. (1) Show that V is a subspace of P2 (2) Find a basis of V and the dimension of V
Consider P3 = {a + bx + cx2 + dx3 |a,b,c,d ∈ R}, the set of...
Consider P3 = {a + bx + cx2 + dx3 |a,b,c,d ∈ R}, the set of polynomials of degree at most 3. Let p(x) be an arbitrary element in P3. (a) Show P3 is a vector space. (b) Find a basis and the dimension of P3. (c) Why is the set of polynomials of degree exactly 3 not a vector space? (d) Find a basis for the set of polynomials satisfying p′′(x) = 0, a subspace of P3. (e) Find...
Choose one of the following problems and determine whether the given set (together with the usual...
Choose one of the following problems and determine whether the given set (together with the usual operations on that set) forms a vector space over R. In all cases, justify your answer carefully. a. The set of all n x n matrices A such that A² is symmetric. b. The set of all points in R² that are equidistant from (-1, 2) and (1, -2) c.  The set of all polynomials of degree 5 or less whose coefficients of x² and...
If p(x) and q(x) are arbitrary polynomials of degree at most 2, then the mapping =p(−1)q(−1)+p(0)q(0)+p(2)q(2)...
If p(x) and q(x) are arbitrary polynomials of degree at most 2, then the mapping =p(−1)q(−1)+p(0)q(0)+p(2)q(2) defines an inner product in P3. Use this inner product to find , ||p||, ||q||, and the angle θ between p(x) and q(x) for p(x)=2x^2+3 and q(x)=2x^2−6x.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT