Determine whether each statement makes sense or does not make sense, and explain your reasoning. A system of linear equations in three variables, x, y, and z cannot contain an equation in the form

Chesley
2021-05-11
Answered

Determine whether each statement makes sense or does not make sense, and explain your reasoning. A system of linear equations in three variables, x, y, and z cannot contain an equation in the form

You can still ask an expert for help

rogreenhoxa8

Answered 2021-05-12
Author has **109** answers

The general form of a system in three variables x,y,z has equation in the general form:

If one of the coefficients ck of the variables z is zero, we can isolate y and bring that equation to the form

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 ${x}_{1}-6{x}_{2}+{x}_{3}=5$ .

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=

B.

C.

D. V=

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=

G.

asked 2022-04-12

How would one go about analytically solving a system of non-linear equations of the form:

$a+b+c=4$

${a}^{2}+{b}^{2}+{c}^{2}=6$

${a}^{3}+{b}^{3}+{c}^{3}=10$

Thank you so much!

$a+b+c=4$

${a}^{2}+{b}^{2}+{c}^{2}=6$

${a}^{3}+{b}^{3}+{c}^{3}=10$

Thank you so much!

asked 2021-12-17

Physical meaning of the null space of a matrix

What is an intuitive meaning of the null space of a matrix? Why is it useful?

I'm not looking for textbook definitions. My textbook gives me the definition, but I just don't "get" it.

E.g.: I think of the rank r of a matrix as the minimum number of dimensions that a linear combination of its columns would have; it tells me that, if I combined the vectors in its columns in some order, I'd get a set of coordinates for an r-dimensional space, where r is minimum (please correct me if I'm wrong). So that means I can relate rank (and also dimension) to actual coordinate systems, and so it makes sense to me. But I can't think of any physical meaning for a null space... could someone explain what its meaning would be, for example, in a coordinate system?

What is an intuitive meaning of the null space of a matrix? Why is it useful?

I'm not looking for textbook definitions. My textbook gives me the definition, but I just don't "get" it.

E.g.: I think of the rank r of a matrix as the minimum number of dimensions that a linear combination of its columns would have; it tells me that, if I combined the vectors in its columns in some order, I'd get a set of coordinates for an r-dimensional space, where r is minimum (please correct me if I'm wrong). So that means I can relate rank (and also dimension) to actual coordinate systems, and so it makes sense to me. But I can't think of any physical meaning for a null space... could someone explain what its meaning would be, for example, in a coordinate system?

asked 2021-08-14

Consider the system (*) whose coefficient matrix A is the matrix D listed in Exercise 46
and whose fundamental matrix was computed just before the preceding exercise.

asked 2021-06-23

asked 2021-09-16

Reduce the system of linear equations to upper triangular form and solve.

5x+2y=8

-x+3y=9

5x+2y=8

-x+3y=9

asked 2021-05-08

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