Suppose Q : R? → R is a quadratic form such that Q(x) = 1 for all vectors X E R? Cuch that

Q: Find the domain of the vector function. (Enter your answer using interval notation.) r(t) = (In(t +…

A:

Q: The vectors a and b are such so that a = √10, b = 10 Find the value of lax bl. and a b = 30

A:

Q: Prove that if a is perpendicular to b, then |a +b|^2 = |a|^2 + |b|^2 .

A:

Q: let v = (1, 3, −2) and w = (2, −1, 4). Compute v × w.

A:

Q: Identify the maximum value and the corresponding unite vector of the quadratic form Q = x1 3a²³ —…

A:

Q: Let L be the line passing through the point P(1, 1, 1) with direction vector d=[2, 1, 0]T. Find the…

A:

Q: Determine whether the set of vectors in P, is linearly independent or linearly dependent. S = {-x +…

A:

Q: IP IE Express the vector + =[] y as a linear combination of = [2] -[1] and y=

A:

Q: 2. Determine whether the expression is defined or undefined. If it is defined, then determine…

A:

Q: Show that V1, V2, V3 are linearly independent, but V₁, V2, V3, V4 are not. Then express V4 as a…

A:

Q: Is {x² – 2.x, x²+x, x²} linearly independent dependent? Prove your answer. or

A: Answer

Q: Show that (u×v)· w = u ·(v×w).

A: As we know that, Multiplication is an Associative Property, i.e. (a x b).c=a.(b x c) and Sometimes…

Q: The vector ₹ = −a + 2a expressed in RCS and in terms of þ is

A:

Q: Find ||e − 4f||, assuming that e and f are unit vectors such that ||e + f|| = √3.

A: The step-by-step solution to the given question is ..  we have ,  e+f=3..........(1) we have to find…

Q: ||ī|| = Find the length of the vector = 2 -2 Enter `sqrt(a)' for √Va

A: In this question we will find the Length of the vector.

Q: Let L be the line passing through the point P(-1, -3, -2) with direction vector d=[-1, 1, 1]T. Find…

A:

Q: Show that no linearly independent set of vectors can contain the zero vector.

A:

Q: Represent the following equation functions. (a) (r – h)² + (y – k)² = r²

A: We have given an equation (x-h)2+(y-k)2=r2. Represent given equation as vector valued function.

Q: Let u = 4 h = V= and w= 1 . For what value of h is w in the plane spanned by u am

A:

Q: -4--|--| 9. Find the norm vector of the vectors a =

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Consider the following vectors in R³: 2 = 3 1 2 Which of the following equals |||||| + (T • Ý)Z||?…

A:

Q: 6. Prove that A ·B+ |A x B|< 2|A||B|| for arbitrary vectors A, B and C.

A:

Q: Find the value of k for which the vectors 2 1 2 and -3 5 k are orthogonal. k =

A:

Q: 1 1 Let A = Find the values of a such that A is not diagonalizable 1 1 0 0 1

A:

Q: 8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

A:

Q: Let V₁ = -4 1 | -12 B-B- V2 = 4 -3 11 -5 " and y = For what value of h is y in the plane spanned by…

A: and We have to find the value of .

Q: Show that if PER"×" is an orthogonal projector, then P+ = P.

A:

Q: = ---- -2 8 span of v₁ and v₂? Let V₁ = and y = -5 -3 For what value(s) of h is the vector y in the

A: The given vectors  and .The objective is the find the value of  for which the vector  in the span of…

Q: Verify that (AB)T = BTAT.

A:

Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: Show that if v and w lie in the yz-plane, then v × w is a multipleof i.

A: Both vectors v and w lie in the y-z plane, which means they must have zero magnitude component along…

Q: Let v vector=[−4 −6] and b vector =[8 1 2] (check the image for reference) Is b vector in the…

A:

Q: Find the length of the projection of [−8 −7]onto the vector [−7 5]   Its written vertically…

A:

Q: The dot product of two vectors can be written in the form s+ 18 t. x1 x2 in R" is defined by * ·ý =…

A: