Given vectors u = (5,0,0), v = (-2,–1,0), and w = (3,7,2), a) Determine if the vectors u, v, w are linearly independent (LI) or linearly dependent (LD). b) Suppose the vectors u, v, and w (from above) formed the columns of matrix A, so A = [u v w ]. If A is the coefficient matrix of the system Ax = b, what type(s) of solution(s), if any, do you expect? c) Is it possible to express t = (1,1,1) as a linear combination of u, v, w ?

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Q: Construct six linearly independent 3 by 3 echelon matrices U1, ... , U6.

A: To Find : Construct six linearly independent 3×3  echelon matrices.

Q: Find the matrix A (in terms of B and C ) if (ЗАТ + 4СТВ)Т3 5A - 4B

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Q: We call a matrix B a square root of A if B2 = A.

A:

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.