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Problem 4 Find the span of 1. {1 – x,1+x} in the space of all polynomial...
2. (a) Let P, =Span{1, x, x?, x°, x*} be the collection of polynomial with degree at most 4. Con- sider subspace H = Span{1,x, x*}. Prove that H is a subspace of Pg. Find a basis for the subspace H. (b) Now consider the differential operator D : H P, defined by D(1) = 0, D(x) = 1 and D(x3)=3x2. Why this defined linear operator D:H-P? Is the map Donto? Is the map Done-to-one?
Problem 4 Let V be the vector space of functions of the form f(x) = e-xp(x), where p(x) is a polynomial of degree (a) Find the matrix of the derivative operator D = d/dx : V → V in the basis ek = e-xXk/k!, k = 0, 1, . .. , n, of V. (b) Find the characteristic polynomial of D. (c) Find the minimal polynomial of D n.
Problem 4 Let V be the vector space of functions of...
Find vectors that span the null space of A. [ 1 2 7 A = 4 5 10 7 8 13 span Additional Materials Tutorial -/1 points HOLTLINALG2 4.1.027. Find the null space for A. null(A) = span munca -son- Submit Answer Practice Another Version
22. (a) Find two vectors that span the null space of A 3 -1 2 -4 (b) Use the result of part (a) to find the matrix that projects vectors onto the null space of A. (c) Find two orthogonal vectors that span the null space of A. (d) Use the result of (c) to find the matrix that projects vectors onto the nul space of A. Compare this matrix with the one found in part (a). (e) Find the...
|(1 point) Let -2 -4 -4 -4 A = -3 -6 -6 -6 Find a spanning set for the null space of A. 1 N(A) span - 0 0
|(1 point) Let -2 -4 -4 -4 A = -3 -6 -6 -6 Find a spanning set for the null space of A. 1 N(A) span - 0 0
Problem 4 Let V be the vector space of functions of the form f(x) = e-xp(x), where p(x) is a polynomial of degree (a) Find the matrix of the derivative operator D = d/dx : V → V in the basis ek = e-xXk/k!, k = 0, 1, . .. , n, of V. (b) Find the characteristic polynomial of D. (c) Find the minimal polynomial of D n.
Problem 1. Given the vector space P the basis B -<1,7,',r'> of P, let U - span[1,2]. V-span c and W -spanr x '] Which of the following statements is true? 1. UV = 0 2. UUV is a vector subspace of P -P 3. U nW - and for any vector subspace P of P UW SPP 4. UUW = P. 5. All except statement 3 is false. Problem 2. Consider the function P, R such that f(1-r) -...
Find an explicit description of the null space of matrix A by listing vectors that span the null space. A= 1 -2 -2 -2 O 1 3 4 NO
Find an explicit description of the null space of matrix A by listing vectors that span the null space. 1-2-4-4 0 1 2 5 OC. - ONO Click to select your answer
7. V={[)a620) a vector space! Draw the vector space? Draw the graph and explain why or why not? I. Verify the axiom for polynomial. p(x) = 2t' +31° +1+1 9(x) = 4r +57 +31 + 2 8. p(t)+9(1) € P. 9. p(t)+q(t) = f(t)+p(1) 10. cp(1) EP A subspace of a vector V is a subset H that satisfies what three conditions? 12. Is 0 a subspace of R" 13. Let V, V, E V; show H = span{v. v)...