
1. Let {ü, 7,w, i}, where u = (3,-2), v = (0,4), ū = (-1,5) and i = (-6,4). Find the components of the resultants obtained by doing the following linear combinations. a. r = 2ū - 40 b. š= 3ū – +20 +
Let f(z) = v/4z2-2z + 4 f'(z) = Preview f'(2) = Preview
Let f(z) = v/4z2-2z + 4 f'(z) = Preview f'(2) = Preview
3. Let ū and ū be vectors. Prove that ū x ū is orthogonal to both ū and v.
Al. Let T1(x, y, z) = (1-y+z, 2:0 – y + 2z, 2y + 2). (a). Is T1 one-to-one? (b). Is T onto?
5 3 1 Let ū = < 2,-3> V = <-2,0 > w = <3,3 > Graph vectors ū, ū, and w in standard position with corresponding terminal points, A, B, and C, respectively. (72 point) What is the length of the altitude of AABC from vertex A? (72 point) -5 -3 -1 -1 0 1 3 5 -3 -5
Find the inverse z-transform x[n] of X(z) = (-2z+6z^2)/(-z^2+2z^3) of the first 4 values starting from 0 (z is a complex variable)
4. Find SS, (x – y + 2z ) ds, where S: z = 3, x2 + y2 s 4. Sketch S first then evaluate.
multivarbile calc
Evaluate ff xy, dơ where s is the portion of the paraboloid 2z-4-xr_y, within 2. 3. Find the flux dơ of the vector field F(x,y,z)-(x2y2z)k across the surface of the cone z - x+y* between -0 andz 4, in the downward direction.
Evaluate ff xy, dơ where s is the portion of the paraboloid 2z-4-xr_y, within 2. 3. Find the flux dơ of the vector field F(x,y,z)-(x2y2z)k across the surface of the cone z - x+y* between -0...
3. Let A and B be any nxn matrices. Suppose ū is an eigenvector of A and A+B with corresponding eigenvalues 1 and p. Show that ū is also an eigenvector for B and find an expression for its corresponding eigenvalue. [2]
3. If ū= 4.2,1 and ū= -2.2.1), find a vector in R3 that is orthogonal to both ū and . Answer: 4. Let A, B and C respectively denote the points (1,1,2), (-3, 2, 1) and (4, -2, -1). Find AB, AC and AB X AC. Answer: AB= AC = 1. AB X AC = 5. (a) Find the equation of the plane containing the points A, B and C above. Answer: (b) Check that your answer to (a) above...