5. Determine whether vectors u =(2,-6,-5), v = (3,8, 18) and w = (8,-6,7) will form a basis for R³. Justify your answer.

Q: Find the sum of the vectors (–1,4) and (6, –2) and illustrate geometrically.

A: A vector V→=a,b can be represented on the cartesian plane, From the vector law of addition,…

Q: Show whether or not the set of vectors B = {U, V, W} where U = V = and W = 0 is a basis for R³.

A:

Q: Find a vector orthogonal to both and . Include a step by step solution please

A:

Q: 7. Show that the vectors A=4a, -2a + 2a, and B = -6ā, +3ā, -3ā. e parallel to each are other.

A:

Q: Determine if the vectors , and are linearly independent.

A:

Q: Consider the vectors A= (4, -2, 2), B =-(-2,3,0), and C= (0, 2, 1). 1. Find the following. (a) B- A…

A:

Q: 1. Determine whether the points A(3,4,-1) and B(1,-1,0) lie on the line with vector equation…

A: Given vector equation :

Q: Determine whether the vectors (1,2,3), (5,6,7), (9,10,11), and (4,8, 12) are linearly independent.

A:

Q: Find a vector perpendicular to (2, −1, 10) and (1, 2, −1)

A:

Q: Consider the vectors i = (6,4), i = (-2,6), = (4, 2), and i = (-2, 3). Which of these vectors are…

A:

Q: ● Let A = (1.-2,4), B (0,3,2), C (-1,4,-2) be three points in R. Find the vectors u-AB and v-AC.

A: Let A=(1, -2,4), B=(0,3,2), C=(-1,4,-2) be three points in R3. We have to find the vectors u and v.

Q: ) The vectors (3,0,0,0), (0,−1,2,1), (6,2,−6,0) and (3,−2,3,3) in ?4 are linearly independent.

A: solve the following

Q: Let a = (a1, a2), b = (b₁,b2) be vectors in R². The area(a, b) is given by 1b₂-a2b₁. (a.) Show that…

A:

Q: 5. Sketch the given vectors Vand W. On your sketch, draw in v v+w, and v-w. OV=(2, 1) and W=(1, 2)…

A:

Q: Let the following vectors be in R³ a = (1,3,-1) b = (-2,1,3) c = (3,2,1) d= (1,-1,2) 14.- Perform…

A:

Q: Find two vectors a and b such that projba = <4, -2, 8>. That's all the information I was…

A: It is given that,

Q: Let the following vectors be in R³ a = (1,3,-1) b = (-2,1,3) c = (3,2,1) d= (1,-1,2) 12- Find the…

A: