please help. system is sensitive to answers. Find the coordinate vector (x]a of the vector x relative to the given basis B. 16 and B = (b, b2} b = b2 -4 -2 -5 28 O A. -64 -196 ов. -32 -64 32 D. 41 5. Find the vector x determined by the given coordinate vector [x]g and the given basis B. -2 -3 -3 -3 -5 -3 - 11 ОВ. хв - 20 18 OA X= 33 - 15...
Problem 1: consider the set of vectors in R^3 of the form: Material on basis and dimension Problem 1: Consider the set of vectors in R' of the form < a-2b,b-a,5b> Prove that this set is a subspace of R' by showing closure under addition and scalar multiplication Find a basis for the subspace. Is the vector w-8,5,15> in the subspace? If so, express w as a linear combination of the basis vectors for the subspace. Give the dimension of...
Consider the following generic reaction: A+2B→C+3D, with ΔH = 111 kJ . Determine the value of ΔH for each of the following related reactions. A. 3A+6B→3C+9D B. C+3D→A+2B C. 1/2C+3/2D→1/2A+B
At 150 K the reaction below has K. = 4.8*10-12 A + 2B + C + 2D You start the reaction with [A] = 6.6 M, [B] = 1.7 M, [C] = 0.0 M and [D] = 0.0 M a. If you let the reaction come to equilibrium what will [D] be? (8 points) b. What is K. for the following reaction at 150 K. (6 points) 3C + 6D 3A + 6B
Let A be the abelian group with generators a, b, c, d and relations 2a 4b + с, 4c-d-2b and a + b + c + d-0. Write A as the cartesian product of cyclic groups as in the classifaction theorem Let A be the abelian group with generators a, b, c, d and relations 2a 4b + с, 4c-d-2b and a + b + c + d-0. Write A as the cartesian product of cyclic groups as in the...
Problem 1: Consider the vectors À and B shown below. Let R- 3A - 2B. B 2 40° 10 a) Use graphical addition to roughly sketch the resultant vector R. Your sketch does not need to be to scale. b) Using algebra, find the components R, and R, of the resultant vector. Express R using the unit vector notation.
Problem 3 (10pt). Consider the sets V1 = {[a, b, c, d]T E R*: a+c=0}, V2 = {[a, b, c, d]T ER+ : a+c= 0,b+d=1}, V3 = {[a,b,c,d)' e R+ : ac =0}. Decide if V1, V2, V3 are subspaces of R4. Explain. Bonus (5pt). If one of V1, V2, V3 is a subspace find a basis for it and find its dimension.
Let A be the abelian group with generators a, b, c, d and relations 2a 4b + с, 4c-d-2b and a + b + c + d-0. Write A as the cartesian product of cyclic groups as in the classifaction theorem Let A be the abelian group with generators a, b, c, d and relations 2a 4b + с, 4c-d-2b and a + b + c + d-0. Write A as the cartesian product of cyclic groups as in the...
la b c Given that d e f =-1 , find 18 hill | 2a 2b 2c -2d -2e | 6g 6h 6i || 2a 2b 2c | |-20 -2e -2f= | 6g 6h 6i exact number, no tolerance
Problem 2: Consider the following 2-dimensional linear subspace of R3: X = {(a,b,c) ER’: a+b+c=0}. Define a linear map F: X X by setting F(a,b,c) = (20 – 3b+c, -3a + 2b+c, a +b – 2c). (a) Find the matrix A representing F with respect to the basis 21 = (1,0, -1), 22 = (0,1, -1). (b) Find the matrix A representing F with respect to the basis î1 = (3,1,-4), f2 = (1, -2,1). (c) Find an invertible matrix...