Determine if the following subsets are subspaces: 1. The set of grade 7 polynomials 2. The...

Determine if the following subsets are subspaces:
1. The set of grade 7 polynomials
2. The set of polynomials of degree 5 such that P (0) = 0
3. The set of continuous functions such that f (0) = 2

Expert Solution

Colby Messinger answered 2 years ago

In the following list of subsets of R3 , select the ones that are subspaces of...

In the following list of subsets of R3 , select the ones that are subspaces of R3 (multiple answers). (As usual, incorrect answers will earn you negative points) Entire R3 { (x+y, x-y, y ) | x,y are real numbers } { (x,y,z) | x,y,z are all nonnegative real numbers } { ( x, -x, 2x ) | x is a real number } { (1,1,1) } { (x,y,3) | x,y are real numbers } { (0,0,0) } { (x+1,...

Determine which subsets are subspaces of M 2x2 (R) and prove your answer. a. W =...

Determine which subsets are subspaces of M 2x2 (R) and prove your answer. a. W = {A ∈ M 2x2 (R) | a12 = -a21} b. W = {A ∈ M 2X2 (R) | a12 = 1} c. Fix B ∈ M 2x2 (R). Let W ={ A ∈ M 2x2 (R) | AB = BA

Let M 2,2 be the set of all 2x2 matrices determine whether the following subspaces. A)...

Let M 2,2 be the set of all 2x2 matrices determine whether the following subspaces. A) the set of all 2x2 diagnol matrices B) the set of all matrices with a12 entry C) the set of all 2x2 triangular matrices

1. Suppose ?:? → ? and {??}?∈? is an indexed collection of subsets of set ?....

1. Suppose ?:? → ? and {??}?∈? is an indexed collection of subsets of set ?. Prove ?(⋂ ?? ?∈? ) ⊂ ⋂ ?(??) ?∈? with equality if ? is one-to-one. 2. Compute: a. ⋂ ∞ ?=1 [?,∞) b. ⋃ ∞ ?=1 [0,2 − 1 /?] c. lim sup ?→∞ (−1 + (−1)^? /?,1 +(−1)^? /?) d. lim inf ?→∞(−1 +(−1)^?/ ?,1 +(−1)^? /?)

1. Show that the set of all polynomials of deg=2 is not a vector space over...

1. Show that the set of all polynomials of deg=2 is not a vector space over reals. can this be fixed, can we have a set of polynomials that is a vector space over reals? 2. Show that the set of 2x2 matrices with m_22 = 1 is not a vector space over reals. 3. Show that the set of infinitely-differentiable real functions is a a vector space under pointwise function addition, and pointwise scalar multiplication as defined in class,...

Consider the following subsets of the set of all students: A = set of all science...

Consider the following subsets of the set of all students: A = set of all science majors B = set of all art majors C = set of all math majors D = set of all female students Using set operations, describe each of the following sets in terms of A, B, C, and D: a) set of all female physics majors b) set of all students majoring in both science and art

Determine whether the polynomials form a basis for P3: 1 − 2t ^2 , t +...

Determine whether the polynomials form a basis for P3: 1 − 2t ^2 , t + 2t^3 , 1 − t + 2t^2

For each of the following polynomials, determine the number of the roots that are in the...

For each of the following polynomials, determine the number of the roots that are in the LHP, in the RHP, and on the jw-axis. i. s3 + s + 2 = 0 ii. s4 - 4s3 + 7s2 - 8s + 10 = 0 ** When solving for LHP, RHP, & jw-axis, can you explain what differentiates these different categories? (i.e. I understand that the RHP you need to look for a sign switch but do not understand the LHP...

For the following data set [ 1, 4, 3, 6, 2, 7, 18, 3, 7, 2,...

For the following data set [ 1, 4, 3, 6, 2, 7, 18, 3, 7, 2, 4, 3, 5, 3, 7] please compute the following 1. measures of central tendency (3 points) 2. standard deviation ( 5 points) 3. is 18 an outlier? (5 points) 4. describe the shape of the distribution (2 points)

X and Y are subsets of a universal set U. Is the following statement true or...

X and Y are subsets of a universal set U. Is the following statement true or false? Support your answer with a venn diagram. X - (Y u Z) = (X - Y) n (A - C)

Question