Prove that the permutation symbol (e) defines a Cartesian tensor in R². It is assumed that e is defined in the same way in every rectangular coordinate system. If the change of coordinates is xax, where (a) (a) = (8 pg) and |a₁|= a₁1922912921 = 1 we have to establish the Cartesian tensor law (3.22) ēj=e,sairajs Let's examine separately the four possible cases: (n=2) 1 = ²12 i=j=1 e₁₁ª₁a18 = a11912 912ª911 = 0 = 11 i=1,j-2 e,,a1a28 = a11922-912921 i=2,j=1 e,,azra1s =a21912-a22911 i=j=2 esa₂ra2x=a21922922 921 - 1 = ²21 = - - 0 = €22

Express −i+j in the form [a,b]

Hi, there need help how do I find the correct LCD: 3/x+1  +  2/x2

Solve for the general solution of the equation: 2x’’+ 200x = 0. Show all math steps.

Let u = 6i +6j, v = 3i - j, and w= -7i. Find 5u - (2v - w). 5u - (2v-w) = (Type your answer in terms of i and j.)

Plotthe inverse 11'5-) (-3,-3) (4,-6)

Let A- (a, a2 a3} and B= (b, bz b; be bases for a vector space V, and suppose b, = 2a, - 4az, b,= -a, + 4az, by =a, +az + 3a,. %3D %3D a Find the change of-coordinates matrix from B to A b. Find (x, for x=b, - 2b, + 2b,