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Recent questions in Forms of linear equations

iohanetc 2021-05-05

Write the given system of linear equations as a matrix equation of the form Ax=b.
$x_{1} - 2 x_{2} + 3 x_{3} = 0$
$2 x_{1} + x_{2} - 5 x_{3} = 4$

Chesley 2021-05-03

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. $[\begin{matrix} 1 & 2 & 0 & 0 & | & - 4 \\ 0 & 0 & 1 & 0 & | & - 3 \\ 0 & 0 & 0 & 1 & | & 2 \\ 0 & 0 & 0 & 0 & | & 0 \end{matrix}]$

ankarskogC 2021-05-02

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.

Yulia 2021-05-01

Each of the matrices is the final matrix form for a system of two linear equations in the variables $x_{1}$ and $x_{2}$ . Write the solution of the system. $[\begin{matrix} 1 & 5 & | & 10 \\ 0 & 0 & | & 0 \end{matrix}]$

sodni3 2021-05-01

The coefficient matrix for a system of linear differential equations of the form y′=Ay has the given eigenvalues and eigenspace bases. Find the general solution for the system.
$λ 1 = 2 \Rightarrow {[4, 3, 1]}, λ 2 = - 2 \Rightarrow {[1, 2, 0], [2, 3, 1]}$

smileycellist2 2021-03-04

Write the homogeneous system of linear equations in the form AX = 0. Then verify by matrix multiplication that the given matrix X is a solution of the system for any real number $c_{1}$
${\begin{cases} x_{1} + x_{2} + x_{3} + x_{4} = 0 \\ - x_{1} + x_{2} - x_{3} + x_{4} = 0 \\ x_{1} + x_{2} - x_{3} - x_{4} = 0 \\ 3 x_{1} + x_{2} + x_{3} - x_{4} = 0 \end{cases}$
$X = (\begin{matrix} 1 \\ - 1 \\ - 1 \\ 1 \end{matrix})$

hexacordoK 2021-02-25

Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations ${\begin{cases} 9 x - 3 y + z = 13 \\ 12 x - 8 z = 5 \\ 3 x + 4 y - z = 6 \end{cases}$

emancipezN 2021-02-25

Write the system of linear equations in the form $A x = b$ and solve this matrix equation for x. $- x_{1} + x_{2} = 4$
$- 2 x_{1} + x_{2} = 0$

Tyra 2021-02-11

Let B be a $(4 \times 3) (4 \times 3)$ matrix in reduced echelon form.

a) If B has three nonzero rows, then determine the form of B.

b) Suppose that a system of 4 linear equations in 2 unknowns has augmented matrix A, where A is a $(4 \times 3) (4 \times 3)$ matrix row equivalent to B.

Demonstrate that the system of equations is inconsistent.

EunoR 2021-02-09

Determine whether the given $(2 \times 3) (2 \times 3)$ 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
$x = a t + b, y = c t + d, z = e t + f$
$2 x_{1} + x_{2} + x_{3} = 3$
$- 2 x_{1} + x_{2} - x_{3} = 1$

babeeb0oL 2021-02-08

The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution. $[\begin{matrix} 1 & 0 & - 1 & - 2 & 0 \\ 0 & 1 & 2 & 3 & 0 \end{matrix}]$

Tyra 2021-02-03

Determine whether the given $(2 \times 3)$ 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
$x = a t + b, y = c t + d, z = e t + f .$
$x_{1} + 2 x_{2} - x_{3} = 2$
$x_{1} + x_{2} + x_{3} = 3$

Tolnaio 2021-01-23

The coefficient matrix for a system of linear differential equations of the form $y^{1} = A y$
has the given eigenvalues and eigenspace bases. Find the general solution for the system
$λ_{1} = 2 i \Rightarrow {[\begin{matrix} 1 + i \\ 2 - i \end{matrix}]}, λ_{2} = - 2 i \Rightarrow {[\begin{matrix} 1 - i \\ 2 + i \end{matrix}]}$

Burhan Hopper 2021-01-04

The coefficient matrix for a system of linear differential equations of the form $y^{1} = A y$ has the given eigenvalues and eigenspace bases. Find the general solution for the system

$λ 1 = 3 \Rightarrow [\begin{matrix} 1 \\ 1 \\ 0 \end{matrix}]$

$λ 2 = 0 \Rightarrow [\begin{matrix} 1 \\ 5 \\ 1 \end{matrix}] [\begin{matrix} 2 \\ 1 \\ 4 \end{matrix}]$

Khadija Wells 2020-12-28

Write the vector form of the general solution of the given system of linear equations.
$x_{1} + 2 x_{2} - x_{3} = 0$
$x_{1} + x_{2} + x_{3} = 0$
$x_{1} + 3 x_{2} - 3 x_{3} = 0$

Ava-May Nelson 2020-11-08

The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution.
$[\begin{matrix} 1 & 0 & - 1 & - 2 \\ 0 & 1 & 2 & 3 \end{matrix}]$

cistG 2020-11-02

The coefficient matrix for a system of linear differential equations of the form $y_{1} = A y$
has the given eigenvalues and eigenspace bases. Find the general solution for the system
$λ_{1} = 3 + i \Rightarrow {[\begin{matrix} 2 i \\ i \end{matrix}]}, λ_{2} = 3 - i \Rightarrow {[\begin{matrix} - 2 i \\ - i \end{matrix}]}$

texelaare 2020-11-01

The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution.
$[\begin{matrix} 1 & - 1 & 0 & - 2 & 0 & 0 \\ 0 & 0 & 1 & 2 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \end{matrix}]$

Students dealing with post-secondary Algebra will know that linear equation standard form examples are quite hard to find, let alone obtain solutions to questions related to algebraic problems. Luckily, you will find suitable answers to your linear equation standard form tasks by turning to help based on provided solutions. Even though one may use several calculators online, the college professors will require a verbal or written explanation, which is where provided forms of linear equations answers always help to avoid trouble and see the reasoning.

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