A triangle in space is defined by the points P = (1,1,2), Q = (−1,0,3) and R = (2,1,−1). Find a vector form and the parametric equations for the equation of the line passing through...

A triangle in space is defined by the points P = (1,1,2), Q = (−1,0,3) and R = (2,1,−1). Find a vector form and the parametric equations for the equation of the line passing through...

a) A=[i, 1, 0] [1, 2i, -3i] [1, -1, 1-i] b) A= [1, i, -2] [3, 4i, -5] [-1, -31,...

Use properties of the cross product to calculate the following: (a) (e1+e2)×(e1×e2) = (b) 3e3×(e3+e2) =

Let T: R3 → R4 : [ x, y, z] → [ y, z, x, xyz] Determine whether or not T is a linear transformation from R3 to R4.

Let S = { a0 + a1x + a2xˆ2 : ai ∈ R, a0 + a1 + a2 = 1. Determine if S is a subspace of the vector space of polynomials of degree at most 2 over R.

1. N(A)=C(A) is impossible 2. If N(A) = C(A), then n must be even. 3. If N(A) = C(A), then n must be odd.

Then the dimension of the nullspace of A is ? and the dimension of the left nullspace of A is?

what is the first, second and third component of T(3,1)?

x-y-z=1 x+3y+3z=-1 x+y+z=0

T | a11 a12 | | a11+a22 a12+a21 | | a21 a22 | = | a11+a21 ...

How we can prove that is a subspace ?

Show whether the following three vectors are linearly independent or not V := C(R); f1(x) = ex; f2(x) = e3x; f3(x) = x(x−1) Solution: af1 + bf2...

This is a function of x and is asking to plot this point but I am confused.

Steve is two years older than Marvin, Five years ago the sum of their ages was 10 years more than Steve's present age. How old was Marvin 5 years ago?

Steve is two years older than Marvin, Five years ago the sum of their ages was 10 years more than Steve's present age. How old was Marvin 5 years ago?

Luis can run 10 kph faster than Greta. One day,each of them left their house and ran towards each other. If the distance between them was 43.5 km and they met in 45 minutes, what was their rate?...

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

might help to use dot product and cauchy schwartz inequality

( 1, -1, 2 ) ( 2,0,1) ( -1, 2, -1 ) Is there a way to figure it out by looking at them instead of the matrix way ?

2x+y=2 please help

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