7. Find any two ON (orthonormal) vectors in (a) span {(1,2), (6, -1)} (b) span {(1, 2, 4), (2, -1,3)} - (c) span {(1,-1,0), (1,2,3)}

Q: iii) The area of the parallelogram spanned by the three-dimensional vectors 3 -4 and 2 -5 is Number

A:

Q: Let x(¹) (t) = = -3t e 4e-3t, 0 0 x (²) (t) = [_5e-31]. -5e-3t, 0 Are the vectors x(¹) (t), x(²) (t)…

A:

Q: PLS HELP ASAP ON ALL

A:

Q: Find a subset ofbthebvectors v1=(0,2,2,4), v2=(1,0,−1,−3), v3=(2,3,1,1) and v4=(−2,1,3,2)that forms…

A:

Q: Find the vector in Span{(1,1,1,1), (1,0,2,-1)} that is closest to (1,0,0,0).

A:

Q: Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is…

A:

Q: For what value of m, the vector (m,3,1) a  linear combination of e\index{1}=(3,2,1) and…

A: We have to find the value of 'm' such that  is a linear combination of Assume

Q: Let a = (-4, 3, 4) and b = (-5, 2, 3), then find the decomposition a = a +a of a with respect to b a…

A: Ggg

Q: Prove that the vectors (a1, a2), (B₁, B₂) = R× Rare linearly dependent iff α₁ß2 - α2ß₁ = 0.

A: The given vectors are  and We have to show that the given vector is linearly dependent if

Q: Q1) Find the equation of the plane passing through the point (4,-1,-5) and perpendicular to the…

A: We have to find the equation of the plane passing through the point (4,-1,-5) and perpendicular to…

Q: Find a vector that is orthogonal to the triangle with vertices P=(1,0,0), Q= (0,2,0), R=(1,1,1)

A: RECALL: Orthogonal vector:  Let us consider to vectors a→ and b→ then , cross product of a→ and b→…

Q: Determine whether the vectors v₁ = (1, 6, 0, 0), v₂ = (0, -1, 0, 1), v3 = (0, 0, 1, 1), and v₁ = (1,…

A:

Q: 6- which of the vectors X-(1,2),Y =(0,1),Z =(-2,-4 ) ,W=(-2,1), U=(-6,3) are orthogonal ,in same…

A:

Q: The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain,…

A:

Q: Represent the product [a* · (b* × c)][m* · (n* × p*)] as a sum of such terms, which contain scalar…

A:

Q: Find the length of the projection of 3   onto the vector -3…

A:

Q: (a) is spanned by the vectors 10 Determine whether the vector v = --()-- [] and or not. 8 (a)…

A:

Q: Can you provide a sketch or model of the vector function (x,y,1-(x+y)) and show it passing through…

A: The sketch can be plotted using 3D modelling tools. In the modelling tool, select the appropriate…

Q: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

Q: Find a non-zero vector perpendicular to

A:

Q: Draw the set of all two-dimensional vectors whose 1-norm is equal to 2. For the matrix 7 A = -2…

A: Given: A=700-2

Q: Find a maximal set of linearly independent vectors out of the set {v1 = (1,2, 3, 4), v2 = (2, 3, 4,…

A: From given set of vectors we have to find maximal set of linearly independent factors. Concept: Let…

Q: Prove that a(-3,2) and b (2,-3) form basis vectors in xy plane

A: a set is said to be basis if set is linearly independent and it spans the space.

Q: Which of the following sets of vectors in R' are linearly independent? (a) (-3,0,4), (5,-1,2),…

A: Linearly independent set: The set of vectors x1, x2, ..., xn in a vector space V is said to be…

Q: a. A nonzero vector perpendicular to both [-1. 3, 4] and [-2. -1, 3].  b. The distance from (2, -1,…

A: Let's go through each of the questions:a. To find a nonzero vector perpendicular to both [−1,3,4]…

Q: (a) Suppose that a and b are two unit vectors in R^3, and a·b=11/24. Find the norm of the vector 4a+…

A:

Q: 27 (3) (Projections) Compute the projection of -2 onto the plane spanned by the vectors 2 and

A:

Q: 4. Let V = R³ and let T: V →V be the linear map given by T(r, y, 2) = (2x + z, y – x+ 2, 32) (you do…

A:

Q: Suppose and are vectors such that a × b =(3, 1, 4). What is the cross product of twice of a with…

A: