Now show that any vector of the form X0+Y is a solution. A(X0+Y)=AX0+AY=b+0=b

asked 2021-06-10

Determine whether the given set S is a subspace of the vector space V.

A. V=\(P_5\), and S is the subset of \(P_5\) consisting of those polynomials satisfying p(1)>p(0).

B. \(V=R_3\), and S is the set of vectors \((x_1,x_2,x_3)\) in V satisfying \(x_1-6x_2+x_3=5\).

C. \(V=R^n\), and S is the set of solutions to the homogeneous linear system Ax=0 where A is a fixed m×n matrix.

D. V=\(C^2(I)\), and S is the subset of V consisting of those functions satisfying the differential equation y″−4y′+3y=0.

E. V is the vector space of all real-valued functions defined on the interval [a,b], and S is the subset of V consisting of those functions satisfying f(a)=5.

F. V=\(P_n\), and S is the subset of \(P_n\) consisting of those polynomials satisfying p(0)=0.

G. \(V=M_n(R)\), and S is the subset of all symmetric matrices

A. V=\(P_5\), and S is the subset of \(P_5\) consisting of those polynomials satisfying p(1)>p(0).

B. \(V=R_3\), and S is the set of vectors \((x_1,x_2,x_3)\) in V satisfying \(x_1-6x_2+x_3=5\).

C. \(V=R^n\), and S is the set of solutions to the homogeneous linear system Ax=0 where A is a fixed m×n matrix.

D. V=\(C^2(I)\), and S is the subset of V consisting of those functions satisfying the differential equation y″−4y′+3y=0.

E. V is the vector space of all real-valued functions defined on the interval [a,b], and S is the subset of V consisting of those functions satisfying f(a)=5.

F. V=\(P_n\), and S is the subset of \(P_n\) consisting of those polynomials satisfying p(0)=0.

G. \(V=M_n(R)\), and S is the subset of all symmetric matrices

asked 2021-07-04

asked 2021-09-15

Write the given system of linear equations as a matrix equation of the form
Ax=b.

x1−2x2+3x3=0

2x1+x2−5x3=4

x1−2x2+3x3=0

2x1+x2−5x3=4

asked 2021-09-11

asked 2021-09-20

Write the solution in vector form. \(\begin{bmatrix}1 & -3 & 2 & 0 & 4 & 0 \\0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 0\end{bmatrix}\)

asked 2021-05-23

The reduced row echelon form of a system of linear equations is given.Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1,x2,x3,x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution.