Consider the matrix attatched and the vector u = (2 0)*. Let B=(A−AT)2 and define vector v = Bu. If v = (v1 v2)*, Write down the value of v1 (the top value from the vector v)     u = (2 0) is 2 on top and 0 on bottom in a vector bracket* v = (v1 v2) is v1 on top and v2 on bottom in a vector bracker*

Q: i) Using Gaussian Elimination method, verify that x, = 2, x2 = -1, and x3 = 3. ii) Show that b is in…

A:

Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

A:

Q: Determine if the vectors are Linearly Independent or Linearly Dependent. -2 [1 -5 =|2.X2) = -3 ,x6)…

A: A set of n vectors of length n is linearly independent if the matrix with these vectors as columns…

Q: is the sum of 2 vectors with components and . What is a?

A: To find the value of a, you can use the properties of vector addition.Given that the sum of the…

Q: Are vectors a = (2, 1, 3) and b = (2, -5, 1) orthogonal? %3D %3D

A:

Q: Let a = (2,3,6) and b = (3,4,2) be vectors.  Compute the cross product aXb

A:

Q: Define how to combine vectors using matrices.

A: To Explain: how can we combine vectors using matrices.

Q: Write N(A) as the span of a vector (r vectors). What is dimN(A)? Why?

A: Null space, N(A) is the set of all vectors x in R^4 here, which are solutions of the equation Ax=0,…

Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

A:

Q: Express vector t = (3, 6, -6, 9) as a linear combination of vectors u = (-1, 3, 0, 7) and v = (-5,…

A: The given vectors are: t=3, 6, -6, 9u=-1, 3, 0, 7v=-5,0, 6, 5 We have to express the vector t as a…

Q: Which of the following sets of vectors are linearly dependent? (i) {(2,3), (-4,-6)}; (ii) ((0, 4,0,…

A:

Q: Find the Values of for which vectors linearly dependent the are -3 4 -5 8. 6. - 2 6. -8

A: Given that three vectors are linearly dependent.

Q: Let a = (7, 10, 1) and b = (10, 3, 6) be vectors. Compute the cross product %3D ахЬ.

A:

Q: Find four different nonzero vectors that are orthogonal to v = (-1,5,2)

A: This is a simple problem based on orthogonal vector which could be solved by using basic knowledge…

Q: Find a vector orthogonal to both (-3, 2,0) and to (0, 2, 1) of the form (1,

A:

Q: find a vector that is orthogonal to (1,2,3) and (4,5,6). do not use cross product.

A: Let's find vector that is orthogonal to given two vectors.

Q: f possible express the vector v as a linear combination of 1, V2, and V3. b) v = (0, 0, -1), V₁ =…

A:

Q: Show that the column vectors (1,1,2,4),(2,-1,-5.2) (1,-1,-4,0) and (2,1,1,6) vectors in R are…

A:

Q: Find a vector orthogonal to both ⟨1,−10,0⟩ and to ⟨0,7,4⟩ of the form

A:

Q: Find two different combinations of the three vectors u = (1,3) and v = (2,7) and w = (1,5) that…

A:

Q: determine if the following pair of vectors is linearly dependent or linearly independent. show all…

A: Step 1: Step 2: Step 3: Step 4:

Q: Define the term column vector.

A: Column Vector is defined as a column matrix representing the elements of any vector written in…

Q: If possible express the vector v as a linear combination of V1, V2, and V3. (b) v = (0, 0, -1), V₁ =…

A:

Q: Let be the vector with initial point (4, 7) and terminal point (8,4). Express as a linear…

A: The objective of this question is to express the vector v as a linear combination of the standard…

Q: (1) S={(2,-1,3), (5,0,4)} (a) u=(1,1,-1) (b) w=(1,-8,12)

A:

Q: Show that the column vectors (1,1,2,4), (2,-1.-5.2), (1.-1,-4,0) and (2,1.1,6) vectors in R are…

A:

Q: What helps to set of vectors linearly independent?

A: