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Determine whether or not the given vector field is conservative. If its conservative find f such that F=delta f
1.) F(x,y,z)= yi + xj + k
2.) F(x,y,z)= zxi + xyj + yzk
If you were to let A be a 6 x 14 matrix where the dimension of the row space is 3 (dim(R(A) = 3), what would the dimension of the null space of matrix A (dim(N(A)) be and what would the dimension of the null space of A^T (dim(N(A^T)) be?
Find the vertex.
Let G = UT (n,F) be the set of the upper triangular n x n matrices with entries in a field F with p elements and 1's on the diagonal. The operation in G is matrix multiplication.
Computer analysis showed that the surface of a certain drumlin can be approximated by y= 10(1-0.0001x^2) revolved 180 about the x-axis from x= -100 to 100.
Prove that a graph G is a forest if and only if every induced subgraph of G contains a vertex of degree at most 1.
Prove the parallelogram equality that is, the sum of the squares of the diagonals of a parallelogram equals the sum of the squares of its sides.
Determine the intervals on which 'f ' is concave up and the intervals on which 'f ' is concave down. Find the values of all local minima and local maxima of 'f '. Explain why each value you find is a minimum or a maximum.
The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.
Estimating the value of a function using 3rd Taylor polynomial and use our error guarantee to give a Plus- or-minus error to your estimate
Linear Transformations, Rotations, Submodules and Subspaces, (7) Let F=R, let V=R^2 and let T be the linear transformation from V to V which is rotation clockwise about the origin by pi-radians. Show that every subspace of V is an F[X]-submodule f..
Find the slope and y intercept of the line. Graph the line 7x-5y=35. Decide whether the given linear equations are parallel, perpendicular or neither. y=4x+9 y=-1/4x+5/4
Suppose that G is a forest Consisting of k trees T1, T2, ..., Tk. Furthermore, suppose that Ti has order ni, for 1 Is the n-dimensional cube Qn Hamiltonian? Prove your answer.
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