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In each part use the information in the table to find the dimension of the row space, column space and null space of A and the null space of AT.
Let V be the space of all functions from R to R. It was stated in the discussion session that this is a vector space over R
Using the given vectors how do I find the specified dot product u=3i-8j;v=4i+9j find u.v
Two opposite vertices of a square are P(3, 2) and Q(-5, -10). Find the length of: a diagonal of the sqaure
Prove that the origin is the only "corner" of P. [You may show it is the only vertex, extreme point, or basic feasible solution.]
Find an orthonormal set : {f_o, f_1} in V such that span{e_o,e_1} = span{f_o,f_1}, where e_o(x) = 1 and e_i(x) = x.
Given the parabola y = -(x - 6)2 - 1, determine each of the following: Identify whether the parabola y = -(x - 6)2 - 1 opens up or down.
A force of 703 pounds is needed to push a stalled car up a hill inclined at an angle of 16-degrees to the horizontal. Find the weight of the car.
A kite string exerts a 12-lb pull (F=12) on a kite and makes a 45° angle with the horizontal. Find the horizontal and vertical components of F.
A baseball is hit from a height of 3 feet with an initial speed of 120 feet per second at an angle of 30 degrees above the horizon.
A weight of 850 pounds is suspended by two cables. One cable makes an angle of 66 degrees with a vertical line, the other makes an angle.
Explain in your own words when the elimination method for solving a system of equations is preferable to the substitution method.
Find the arc length of the curve given by x = cos 3t, y = sin 3t, z = 4t, from t = 0 to t = pi/2.
Given f(x,y,z)=x^2y^3z^6, in what direction is F(x,y,z) increasing most rapidly at the point P(1,-1,1). What is the rate of increase?
Given F = 4i -2k;..... P(0,1,0) and Q(4,0,1) find the work W done by the force (F)moving a particle in a straight line from P to Q.
A quadratic model for the data (calculated using regression on your calculator). Be sure to be clear about what each of your variables represents.
Let F be a field, V a vector space over F, and v1,...,vk vectors in V. Prove that the set Span({v1, ..., vk}) is closed under scalar multiplication.
Find the equation of a plane through the origin and perpendicular to: x-y+z=5 and 2x+y-2z=7
Let F be the field of real numbers and let V be the set of all sequences , (a1 , a2 .....,an ,......) , ai ? F where equality, addition.
Compute the divergence and curl of v. Show that v is neither the gradient of a function nor the curl of a C2 vector field.
A certain professor has a file containing a table of student grades, where the first line of the file contains the number of students.
Let n be a positive integer. Let A be an element of the vector space Mat(n,n,F), which has dimension n2 over F.
Show that the functions (c1 + c2sin^2x + c3cos^2x) form a vector space. Find a basis for it. What is its dimension?
If g(x,y)= x-y^2, find the gradient vector (3,-1) and use it to find the tangent line to the level curve g(x,y)= 2 at the point (3,-1).