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Let u, v, w, x in R^2 be vectors. If u is a linear combination of v and w and v is a linear combination of w and x, show that u is a linear combination of w and x

(i) Find the parametric equation of the line l through the point (2, 2, −2) and parallel to the line x = 2 − 7t, y = 3 + 4t, z = −t, t ∈ R.   (ii)Calculate the equation of...

Find the equation of the plane which contains the point ( 2/3, −1, 3) and has normal vector 3i − 2j + 9k. Also, find another two points on this plane which are different from ( 2/3, −1,...

Find the parametric equation of the line which contains the point ( 1/2, 0, −3) and is parallel to the vector 2i − 4j + k. Also, find another point on this line which is different from...

I am studying linear algebra, I have come across a question to which i am confused. The question is Which of the following set of vectors is linearly independent? (i^,j^,k^ denote the unit vectors...

there are two red jars of marbles and one jar of blue marbles.  Jars of the same color of marbles contain the same number of marbles in them.  there are 35 total marbles.  The difference...

Im not to sure how to do this problem. I think it has to do with fields, but not sure. the question asks    express 1/(4+4P^1/3 + 5P^2/3) in the form of x+yP^1/3 +...

No additional details, the question is a true/false question.

Given vectors u, a, v, and b as defined below, let T : R2 → R2 be a linear transformation that maps the vector u to the vector a and the vector v to the vector b. Use the linearity of T to find the...

Given the matrix A and the vector b below, define the transformation T : R3 → R3 by T (x) = Ax. Determine whether or not b is in the range of T. If so, find a vector x such that T(x) = b.  ...

10. For v1, v2, and v3 as defined below, determine whether or not the set {v1, v2, v3} is linearly independent.           1            -3...

Given A and b as defined below, write the general solution of Ax = b in parametric vector form.        2  -5   3             -1 A...

Consider the following matrices. A= -3  1    and B=0   4        0  2              -1  6 (a) Find -2A+B (b)...

Given the sizes of two matrices A and B, determine the sizes of the product AB and the product BA, if the products are defined. Worth 8 points. (a) Ais4×4andBis4×4. (b) Ais2×1andBis1×1. (c)...