Question

In: Math

Do the following sets of vectors span R^3? 1) [1,3,1], [3,9,4], [8,24,10], [-10,-30,-13] 2) [1,2,3], [-1,-2,-4],...

Do the following sets of vectors span R^3?

1) [1,3,1], [3,9,4], [8,24,10], [-10,-30,-13]

2) [1,2,3], [-1,-2,-4], [1,2,2]

3) [-1,-3,-1], [-4,-12,-3]

4)[1,2,-2], [7,5,7], [-4,-1,-11]

Solutions

Expert Solution


Related Solutions

Determine which of the following sets of vectors form a basis for R 3 . S...
Determine which of the following sets of vectors form a basis for R 3 . S = {(1, 0, −1),(2, 5, 1),(0, −4, 3)}, T = {(−1, 3, 2),(3, −1, −3),(1, 5, 1)}.
What do the following credit terms mean? 1. n/30 2. 2/10, n/30 3. n/10 EOM 4....
What do the following credit terms mean? 1. n/30 2. 2/10, n/30 3. n/10 EOM 4. n/20 5. 1/10, n/20 6. 3/5, n/30 7. n/15 EOM Have you seen any of these in your work place?
#1 Let H= Span{v1,v2,v3,v4}. For each of the following sets of vectors determine whether H is...
#1 Let H= Span{v1,v2,v3,v4}. For each of the following sets of vectors determine whether H is a line, plane ,or R3. Justify your answers. (a)v1= (1,2,−2),v2= (7,−7,−7),v3= (16,−12,−16),v4= (0,−3,−3) (b)v1= (2,2,2),v2= (6,6,5),v3= (−16,−16,−14),v4= (28,28,24) (c)v1= (−1,3,−3),v2= (0,0,0),v3= (−2,6,−6),v4= (−3,9,−9) #2 Plot the linesL1: x= t[4−1] and L2: x= [−4−2] + t[4−1] using their vector forms. If[12k]is onL2. What is the value of k?
For what values of k (if any) do the following three vectors span (a) a line,...
For what values of k (if any) do the following three vectors span (a) a line, (b) a plane, or (c) all of R3? (1, 2, 3),(3, k, k + 3),(2, 4, k)
Are the vectors v1 = (1 , 2, 3), v2 = (2, 4, 6), and v3...
Are the vectors v1 = (1 , 2, 3), v2 = (2, 4, 6), and v3 = (1, 1, 3) linearly independent or dependent? Since v2 is a scalar multiple of v1, both v1 and v2 are linearly dependent, but what does that say about the linear dependence of the three vectors as a whole?
1) Determine the angle between vectors: U = <2, -3, 4> and V= <-1, 3, -2>...
1) Determine the angle between vectors: U = <2, -3, 4> and V= <-1, 3, -2> 2) determine the distance between line and point P: -2x+3y-4z =2 L: 3x – 5y+z =1 3) Determine the distance between the line L and the point A given by L; (x-1)/2 = (y+2)/5 = (z-3)/4 and A (1, -1,1) 4) Find an equation of the line given by the points A, B and C. A (2, -1,0), B (-2,4,-1) and C ( 3,-4,1)...
consider the following state vectors |psi subscript 1> =3|+> + 4|-> |psi subscript 2> = |+>...
consider the following state vectors |psi subscript 1> =3|+> + 4|-> |psi subscript 2> = |+> + 2i |-> |psi subscript 3> = 3|+> - e exp ipi\3 |-> Now , normalize each state vector then , For each state vector calculate the probability that the spin components is up or down along each of the three cartesian axes . Use bra-ket notation for the entire calculation.
1. calculate the standard deviation for the following returns: -10, 10, 13, -4, 5 2. a...
1. calculate the standard deviation for the following returns: -10, 10, 13, -4, 5 2. a stock has an expected return of 13.5%, its beta is 1.17 and the risk-free rate is 5.5%. what must the expected return on the market be? 3. Systematic Risk is fully diversifiable (T/F)
Consider the following time series. t 1 2 3 4 5 yt 6 10 8 13...
Consider the following time series. t 1 2 3 4 5 yt 6 10 8 13 15 (a) Choose the correct time series plot. (i) (ii) (iii) (iv) What type of pattern exists in the data? (b) Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. If required, round your answers to two decimal places. y-intercept, b0 = 4.1 Slope, b1 = 2.1 MSE = ???? (c) What is the...
Consider the data. xi 1 2 3 4 5 yi 3 7 5 10 13 (a)...
Consider the data. xi 1 2 3 4 5 yi 3 7 5 10 13 (a) Compute the mean square error using equation s2 = MSE = SSE n − 2  . (Round your answer to two decimal places.) (b) Compute the standard error of the estimate using equation s = MSE = SSE n − 2  . (Round your answer to three decimal places.) (c) Compute the estimated standard deviation of b1 using equation sb1 = s Σ(xi −...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT