H={[a,b,c,d]: a+3b=c, b+c+a=d} Show the subset H is a subspace or give a counter example I am very confused can someone help

H={[a,b,c,d]: a+3b=c, b+c+a=d} Show the subset H is a subspace or give a counter example I am very confused can someone help

Determine whether the given set is a subspace of P3. Explain why. A = {p(t) = at^3+bt} Where a and b are both elements of the Reals.

Given a 4x4 matrix where R1: a b c d, R2: e f g h, R3: i j k l, R4: m n o p. We know that the determinant of this matrix is 9. What would the new determinant be if the matrix was transformed into...

How to determine whether the vectors u:(1,-1,4) , v:(-2,1,3) , w:(4,-3,5) span R^3 ???

Per example, these are operators that do not preserve the addition: Ln (a+b) is not = ln a + ln b like (a+b)^3 is not = a^3 + b^3 Maybe...

Please Help! An approximate linear model that gives the remaining distance, in miles, a plane must travel from San Diego to Brussels is given by the function: s(t) = 6000 - 500t (12hrs) where s(t)...

Let T: R2→R2 be the linear transformation that first rotates points clockwise through 30∘ and then reflects points through the line y=x. Find the standard matrix A for T. A = [] ?...

Assume u4 is not a linear combination of {u1,u2,u3} A. {u1,u2,u3,u4} is never a linearly dependent set of vectors. B. {u1,u2,u3,u4} could be a linearly independent or linearly...

Determine whether or not TT is onto in each of the following situations: 1. r<s 2. r>s 3. r=s A. T is not onto. B. T is onto. C. There is...

W1= First row is ( a , a+b ) Second row is ( c , b ) W2= First row is ( d , 2d) Second row is 3e , e) I know that intersection just means whats common in both but I dont...

x,y,z ∈ ℝ3 and x+y+3z=0 How do I prove ax+by+cz=dx+ey, if d and e are real numbers chosen to fit the equation? Thank you very much if...

Let P3(R) be the vector space of all real polynomials of degree less than or equal to three. Let T be a linear operator on P3(R) defined by T(f(x)) = f'(x) + f′′(x), where f′(x) is the differentiation...

It is for linear algebra and has to do with vectors and the relatonship between them

V=C(TR) f1 (x)=ex f2 (x)= e3x f3 (x)= x(x-1)

Let x= 6 -4 -2 and y= -6 0 4 v = u = w =

the vector [-14,-7,19] is a linear combination of vectors [-3,-3,-3] and [10,9,-10] if and only if the matrix equation Ax = b has a solution x where A = [? ?] and...

You have a subscription to a music downloader that cost $16 dollars a month. This subscription allows you to download 30 songs a month. Find the slope of the line

I am asked to turn it into a sum of squares (so that I can affirm that no matter the value of v1,v2,u1,u2, the answer to the formula will be positive). How do I turn this, or any expression, into...

The set of all upper triangular nxn matrices is a subspace W of Mnxn (F). Find a basis for W . What is the dimension of W ?

Prove that a subset W of a vector space V is a subspace of V if and only if W ≠empty and whenever a∈ F and x,y ∈W then ax∈W and x+y∈W