Determine whether the given (2 times 3) system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two

Tyra 2021-02-03 Answered
Determine whether the given (2 × 3) system of linear equations represents coincident planes (that is, the same plane), two parallel planes, or two planes whose intersection is a line. In the latter case, give the parametric equations for the line, that is, give equations of the form
x=at + b, y=ct + d, z=et + f.
x1 + 2x2  x3=2
x1 + x2 + x3=3
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

i1ziZ
Answered 2021-02-04 Author has 92 answers
Step 1
The given system of linear equations
x1 + 2x2  x3=2
x1 + x2 + x3=3
We need to determine whether the given system of linear equations represents coicident planes, two parallel planes, or two planes whose intersection is a line.
Let n1=(1, 2, 1) and n2=(1, 1, 1,) be normal vectors of both the equations.
Then n1 and n2 are not parallel.
Let x3=t then replace x3=t in the system of linear equations
x1 + 2x2  t=2(1)
x1 + x2 + t=3(2)
(1) x1=2  2x2 + t
Replace x1=2  2x2 + t in the second equation
2  2x2 + t + x2 + t=3
x2=1  2t
x2=2t  1
Replace x2=2t  1 and x3=t  x1=2  2x2 + t, then
x1=2  2(2t  1) + t
=2  4t + 2  t
=3t + 4
Hence, the plane intersect in a line and the parametric equations are
x1= 3t + 4, x2=2t  1 and x3=t
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-06-10
Determine whether the given set S is a subspace of the vector space V.
A. V=P5, and S is the subset of P5 consisting of those polynomials satisfying p(1)>p(0).
B. V=R3, and S is the set of vectors (x1,x2,x3) in V satisfying x16x2+x3=5.
C. V=Rn, and S is the set of solutions to the homogeneous linear system Ax=0 where A is a fixed m×n matrix.
D. V=C2(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=Pn, and S is the subset of Pn consisting of those polynomials satisfying p(0)=0.
G. V=Mn(R), and S is the subset of all symmetric matrices
asked 2021-09-24

Each of the matrices is the final matrix form for a system of two linear equations in the variables x1 and x2. Write the solution of the system.

[10|301|5]

asked 2021-05-16

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;x,y; or x,y,z;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. ⎡⎣⎢100010430420⎤⎦⎥

asked 2021-09-19

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Tell whether the system has one solution, no solution, or infinitely many solutions. Write the solutions or, if there is no solution, say the system is inconsistent. [1001010300140000]

asked 2021-09-27
Consider a consistent system of three linear equations in three variables. Discuss the nature of the system and its solution set if the reduced form of the augmented coefficient matrix has
A) One leftmost 1
B) Two leftmost 1s
asked 2021-09-13
Determine whether the statement is true or false. If the last row of the reduced row echelon form of an augmented matrix of a system of linear equations has only zero entries, then the system has infinitely many solutions.
asked 2021-10-02

Find 63×62