3 ā = |k|,b= |2 -1,c= |k %3D For what values of k do ā, b and č span all of R³? Give a sentence (or two) that explain why your calculations justify your answer. This is equivalent to asking for what values of k are the vectors ā, b, č linearly independent. а,

Q: 7. What is the cross product (Ax B) of the given vectors below? A = -4i + 7j B = 3i

A: Answer of mathematics: Given: log3x2=log3(7x-10) Since base of log are same therefore: x2=7x-10…

Q: a) Determine the magnitude of a vector perpendicular to both n1⇀ =(-3,1,0) n2⇀ =(1,5,2) b) Describe…

A: The given vectors aren1→=-3,1,0= -3 i+1 j+0 kn2→=1,5,2=1 i+5 j+2 k

Q: 4. Three collinear vectors, a, b, and c, are such that à = 2²/b b and à = 1/2c. (a) Determine…

A: The objective of the question is determine the knowns.

Q: Q3 Let A(1,0,-1), B(-1,2, 1), and C(1,2,-2) are the three points in a 3D coordinates system. a)…

A:

Q: a+c] a) Let S = a -b b R. Find three vectors in R3 so that each vector %3D [b-al in S can be written…

A: As this is multiple number of questions. According to our company guide lines, we should answer only…

Q: E a + c] a) Let S Find three vectors in R3 so that each vector in S can be written as a linear…

A: This question is related to linear algebra.

Q: The zero vector 0 (0, 0, 0) can be written as a linear combination of the vectors V1, V2, and v3…

A:

Q: Give an example of a linear combination that resulted in the zero vector that did NOT have 0's for…

A: We need to give an example  of a linear combination that resulted in the zero vector that did NOT…

Q: (c) Give an example of a linear combination that resulted in the zero vector that did NOT have O's…

A: We need to give an example of vectors whose sum with some non zero weights equate to zero. This can…

Q: Find the best approximation to z by vectors of the form c,v, + C2V2. 3 1 - 6 2 - 1 V2 = - 3 3 1 The…

A: Solution

Q: 3. Find the dot product of the vectors d = (-5, 3) and 7 = (1,7).

A:

Q: (c) Give an example of a linear combination that resulted in the zero vector that did NOT have O's…

A:

Q: b) Find values of h for which the vectors are linearly dependent. Justify your answer. 5

A:

Q: Q3 Let A(1,0,-1), B(-1,2, 1), and C(1,2,-2) are the three points in a 3D coordinates system. a)…

A: We have to compute the cross product and find if it is perpendicular to both vectors.

Q: 2. Suppose that you have a circular clock of radius 1, and 12 vectors are placed so that their tails…

A: Given that a circular clock of radius 1 and 12 vectors are placed such that their tails are at the…

Q: Which option is the right? Two vectors are linearly dependent if: -They have the same address -They…

A: Two vector are linearly dependent if in linear combination of v1 and v2 , not all scalar are zero

Q: Week 12: Part 1: This exercise will ask you to explore the equality Null(A") = (Col(A))-. Pick a…

A: Explanation-  For the given question, we will consider the standard unit vectors in ℝ4 Let us assume…

Q: 2. Find the value(s) of h for which the following vectors are linearly dependent. Justify your…

A: To find the value(s) of h, we find the determinant of these vectors and then solve for h.

Q: Is every vector in R2 a linear combination of the vectors (1,-2) and (-2,1)? Provide a detailed…

A: Let (a,b) ∈ R2 , We write the (a,b) is the linear combination of the given vector (1,-2) and (-2,1)

Q: Find the value(s) of h for which the vectors are linearly dependent. [1 10. 3 11.-5

A: Given vectors are L.D if

Q: Let A, B and C are vectors of vertex positions of an arbitrary triangle. Show that any point r…

A:

Q: 2. (а) Find all unit vectors orthogonal to both u = 2i – 3j + k, v = -3i + 3j + 2k If a, b, and c +…

A: In the question it is provided two vectors: u=2i-3j+k and v=-3i+3j+2k The objective is to find all…

Q: Q3 Let A(1,0,-1), B(-1,2, 1), and C(1, 2, -2) are the three points in a 3D coordinates system. a)…

A:

Q: -4] Question 2: For what value of "a" the vector v = 3 is linear a -3° combination of the vectors vị…

A: A transformation is called linearly independent when the nullity of the transformation is 0.…

Q: -7 -3 Find out the area of the triangle whose two sides are given by the vectors: V1 and v2 = -5 8 1…

A:

Q: 2. Is it possible to determine a vector i so that vet is a solution to the system 2 X'(t) = (; )…

A: According to question, Given system, X '⇀t = 1243 X ⇀t

Q: 1 4 Give a reason why the vectors 1 are 8 -88 arly dependent. (3 pts) Write one vector as a linear…

A:

Q: Express the indicated vector w as a linear combination of the given vectors v, and v, if this is…

A:

Q: -4] is linear Question 2: For what value of "a" the vector v = 5 -4 and v3 = combination of the…

A: Givenv=-43a and v1=1-1-2 , v2=5-4-7 and v3=-310To find value of a such that v is linear combination…

Q: 8. ... The value(s) of h which makes the vectors linearly dependent is(are) because this will cause…

A:

Q: 2 (6) (G) () 3. 4. 2 3 5. 1

A: Solve it.

Q: Let A, B and C are vectors of vertex positions of an arbitrary triangle. Show that any point r…

A:

Q: Find the value of k for which the vectors and 4 -4 are orthogonal. k =

A:

Q: --8-9--8-- 7 1. Are the vectors u =| and w= 10 independent? 4 12 2 and 3 3 independent? 5 2. Are the…

A:

Q: Are the vectors i = [-4 -3 -3), i [3 -1 -4] and w= [3 0 -3] linearly independent? Choose If they are…

A:

Q: - 3 7 1 h of h which makes the vectors linearly depe ma to separate answers as needed.)

A:

Q: 4. 5. Find the dot product of u =(5,10) and v= (19,-9) Are the vectors u = (12,-3) and…

A:

Q: The surface of a hill is modeled by z = 100 –- 4x² – 2y². When a group of hikers reach the point (-…

A: key ponts ;  let  z=f(x,y)   be a function then  maximum rate of incrasing is along the vector  ∆f…

Q: Find the value(s) of h for which the vectors are linearly dependent. Justify your answer. 4 -2 ry 8.…

A:

Q: Find the value(s) of h for which the vectors are linearly dependent. Justify your answer. -4 2 - 4…

A: Vectors are Linearly Dependent so it (two vector) can be written as a linear combination of third…

Q: 1. For what value(s) of r (if any) is the vector (-2, 14, r) a linear combination of the vectors (2,…

A: We need to find r.

Q: For what values of h are the given vectors linearly dependent? -24

A:

Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v., v, and v…

A:

Q: -4] Question 2: For what value of "a" the vector v = 3 is linear a combination of the vectors vị…

A: Vectors are the quantity that have magnitude as well as direction. Magnitude of vector is equals to…

Q: [a+c] a) Let S = Find three vectors in R³ so that each vector a - b а, b - a in S can be written as…

A:

Q: Consider the set of vectors in R -3 4 S = 1 3 4 6 (a) Is S linearly independent? Justify your…

A: Given S=-4015, -3-104 ,0436

Q: 5 5 5 0 4 4 0 0 4 Then for which column vector b, the equation Ax = bhas a unique solution? Select…

A:

Q: Find the best approximation to z by vectors of the form c,v, + C2V2. 3 3 6 1 V2 = 1 V1 = - 2 4 3 - 2…

A:

Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v,, v,, and v,…

A:

Q: (a) What weights can we choose so that c,r1 + C22 is the zero vector? (b) Are your weights from (a)…

A: Given  x1→ = -11  and  x2→ = 21