3. Consider the vectors [1,2,3] and [-1,4,8]

Q: Express EC by combinations of the vectors a, b and 7.

A: We have to write EC vector in terms of a,b and c

Q: Given the vectorsA = (2,−4) and B = (−3, 6) in R². How many pairs of real numbers r and s satisfy…

A: System of linear equations

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: Add the vectors E = , F=, G .

A:

Q: Suppose vector a= (4, -6, 10) and vector B= (-6, 9, -15). What is a x b?

A: topic - vectors

Q: ri If the vector 2i – 6j is perpendicular to the vector 2 + 5j in R2, what is r?

A:

Q: 123 Write the vector 2 as a linear combination of the vectors 3 4 (6676) 5 4 2

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: Show that the vectors (1,0,1); (-1,2,3) and (0, 1; -1) spans R³

A:

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

A:

Q: Write a = 18 (0, 3, 0) as the sum of two vectors, one parallel and one perpendicular to b = If a = a…

A:

Q: Can 5= (7,14,0) be written as a linear combination of vectors from the set {(1.-2,-1). (0,1,2).…

A: Consider the set S=1,-2,-1, 0,1,2, 3,-1,0 Now we check set S is Linearly independent or not (need…

Q: Determine whether the following three vectors lie on the same line in R?: и, 3 (4,6,8), и, %3 (2,3,…

A: The given vectors lie on the same line. u2=2,3,4u1=4,6,8=2×2,2×3,2×4=2×2,3,4=2u2So, u1=2u2Thus,…

Q: 6. Write as a linear combination of the vectors

A: solving by linear combination of the given three vectors by converting into syatem of equation...

Q: 6. Show that the vectors (1,1,0), (1, 0, 1), and (0,1,1) generate F3.

A: In this question, we will show that the given vectors generate F3 .

Q: If vector (3,2,2) is expressed by a(1,1,-1)+b(0,1,3)+c(1,-1,1), what are the values of a, b, and c ?

A: Given : Vector (3,2,2) is expressed by a(1,1,-1)+b(0,1,3)+c(1,-1,1). That is

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: Find a vector a that has the same direction as (-8, 9,8) but has length 3.

A: The solution is given below

Q: What is (A - B) and |A - B| * A = i + 2j – k, B = -2i + 3j + k |

A: