Show that (1 0) , (0 1) , (i 0) , (0 i) , form a basis for C^2 over R, where i = √ −1.

Show that (1 0) , (0 1) , (i 0) , (0 i) , form a basis for C^2 over R, where i = √ −1.

Write the equation of the line that represents this graph. Show your work or explain how you determined the equations. On the y-axis of this graph it is numbered 50-300, counting by...

Sven has been on a diet for a couple of months now. When he got on the scale this morning, he weighed in at 242.4 lbs, a marked improvement over the 252 lbs that he weighed 16 days ago. (a)...

Given the set of all vectors in R^3 such that ||U||∞ < 10 , does this form a subspace of R^3 ?

Given a vector space V and a subset of that vector space S, if you squint your eyes and only look at those vectors in S, then S is a subspace of V if S itself is a vector space. If you add two...

f is a linear transformation from P2 to R3 whose standard matrix is ...

For the complex numbers w and z, is Im(w+z)=Im(w) + Im(z). Prove

What is the multiplicative inverse of the complex number 0.2∠0.3

Let's say that a and b are independent vectors, while x and y are non-zero scalars. Suppose there is a matrix A = [a xa b...

Consider the following functions F from P1 to R2, where p(t) is an arbitrary element of P1 (that is, a linear polynomial in variable t). Determine whether each function is an isomorphism...

Say there is Q(x)=3x12 + 3x12 + 2x1x2 , where there's a vector x = [x1 x2]T. I need to find a change of variable x=Uy, where y=[y1 y2]T so that...

A mapping ?? : R3 → R3 is defined by ??(??1,??2,??3)=(??1 +??2,??2 +??3,??3 +??1). (i) Show that ?? is a linear transformation. (ii) Write down the standard matrix of ?? with respect to...

L : V → W is a linear transformation, and v1≠ 0, L(v1) = 0, L(v2) ≠ 0, show that v1, v2 are linearly independent.

if det a c b d = 5 what is det 2a 3d ...

Suppose that you can see that a subset of a vector space does not have the zero vector in it. Why is it a trivial consequence of this that the subset is not a subspace?

Is R7 a subspace of R7?

if det a c b d = 5 what is det 2a 3d ...

Prove that in R4 the 1 norm satisfies the triangle inequality, |x+y|≤ |x| + |y|

Given the set of all vectors in R3 such that ||u||∞ < 10, does this form a subspace of R3?

Argue that all functions real-valued defined on the interval [0, 1] (that is, they are only defined on the interval [0, 1], or, in other words, the collection of all functions f :[0,1] ->...

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