Consider the following vectors
a) Test or refute if the set W is linearly independent.
b) Build a base B for polynomials of degree less than or equal
to
c) Write the matrix associated with base B of part b). d) Vector representation of the polynomial f(x)=x in the base B of part b).
Consider the following vectors a) Test or refute if the set W is linearly independent. b)...
(a). Determine whether the set is linearly dependent or independent. Further, if it is linearly dependent, express one of the polynomials as a linear combination of others. (b). Determine whether the set can be considered as a basis of the vector space P2, which is the set of all polynomials of degree not more than 2 under addition and scalar multiplication. (1). B = {1 – 2,1 – 22, x – x2} (Hint: Similar to the matrix case in last...
Consider the polynomials pq (t) = 7+tand pz(t) = 7–12. Is {P1, P2} a linearly independent set in P3? Why or why not? Choose the correct answer below. O A. The set {P1, P2} is a linearly independent set because neither polynomial is a multiple of the other polynomial. O B. The set (P1, P2} is a linearly dependent set because both polynomials have degree less than 3. O C. The set {P1, P2} is a linearly dependent set because...
4 Q1. Consider the following set of vectors3,0 4 (a) Show that these vectors are linearly independent. (b) Do these vectors span a plane? Explain your answer. (c) Is the set a basis for R5? Why, or why not?
4 Q1. Consider the following set of vectors3,0 4 (a) Show that these vectors are linearly independent. (b) Do these vectors span a plane? Explain your answer. (c) Is the set a basis for R5? Why, or why not?
suppose that s=(v1,v2,......vm) is a finite set of linearly independent vectors in V, and w ∈ V some other vector. Let T= S ∪ (W). Prove that T is not linearly independent if and only if w∈ span(s).
1. (15 points) Prove whether the following sets are linearly dependent or independent, and determine whether they form a basis of the vector space to which they belong. s 10110 -1 ) / -1 2) / 2 1 17 ) } in M2x2(R). "11-21 )'(1 1)'( 10 )'(2 –2 )S (b) {23 – X, 2x2 +4, -2x3 + 3x2 + 2x +6} in P3(R) (the set of polynomials of degree less than 3. (c) {æ4—23+5x2–8x+6, – x4+x2–5x2 +5x-3, x4+3x2 –...
1. Suppose u, V, and w is a linearly independent set (these would have to be non-zero vectors). a. Ifa- u conclusion. v and b-v+ w, is the set (a, b, w] linearly independent? Show the work needed to reach the d b v+ w is the set (a. b,w) linearly independent? Show the work needed to reach the conclustion b. Ifa w v and
3. Consider the following vectors, where k is some real number. H-11 Lol 1-1 a. For what values of k are the vectors linearly independent? b. For what values of k are the vectors linearly dependent? c. What is the angle (in degrees) between u and v? 4. Here are two vectors in R". Let V = the span of {"v1r2} a. Find an orthogonal basis for V (the orthogonal complement of V). b. Find a vector that is neither...
(3) Determine which of the following sets is linearly independent. 02-1 (a) If the set is linearly dependent, express one vector as a non-zero linear combination of the other vectors in the set. (b) If the set is linearly independent, show that the only linear combination of the above vectors which gives the zero vector is such that all scalars are zero. (c) For each of the sets, determine if the span of the vectors is the whole space, a...
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at an orthogonal set of three nonzero vectors u, v, w is linearly independent.
1. Determine whether the following set is linearly independent or not. Prove your clas a. [1+1, 2+2-2,1 +32"} b. {2+1, 3x +3',-6 +2"} 8. Let T be a linear transformation from a vector space V to W over R. . Let .. . be linearly independent vectors of V. Prove that if T is one to one, prove that (un)....(...) are linearly independent. (m) is ) be a spanning set of V. Prove that it is onto, then Tu... h...