# Linear equation forms questions and answers

Recent questions in Forms of linear equations
jernplate8 2021-06-14 Answered

### 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. $$\begin{bmatrix}1 & 0 & -1 & | & 1\\0 & 1 & 2 & | & 1\end{bmatrix}$$

Falak Kinney 2021-06-13 Answered

### Let [A[A b]b] be the augmented matrix of a system of linear equations. Prove that if its reduced row echelon form is [R[R c]c], then R is the reduced row echelon form of A.

Tabansi 2021-06-13 Answered

### 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,x4x as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. ⎡⎣⎢100010000002⎤⎦⎥

Line 2021-06-12 Answered

### The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution. Write the solution in vector form. $$\begin{bmatrix}1&0&0&-3&0 \\0&1&0&-4&0 \\0&0&1&5&0 \\ \end{bmatrix}$$

Efan Halliday 2021-06-10 Answered

### 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

Khadija Wells 2021-06-06 Answered

### 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. $$\begin{bmatrix}1 & -2& | & 7\\0& 0 & | & -9\end{bmatrix}$$

Anonym 2021-06-04 Answered

### The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution. $$\begin{bmatrix}1 & -2&0 & -4 \\0 & 0&1 & 3\\0 & 0&0 & 0 \end{bmatrix}$$

Jaden Easton 2021-06-04 Answered

### The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use $$x,y;x,y;\ or\ x,y,z;x,y,z;\ or\ x_1,x_2,x_3,x_4$$ as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. $$\begin{bmatrix}1 & 0&2&|&-1 \\0 & 1&-4&|&-2\\0 &0 &0&|&-0\end{bmatrix}$$

arenceabigns 2021-06-03 Answered

### Suppose that the augmented matrix for a system of linear equations has been reduced by row operations to the given row echelon form. Solve the system by back substitution. Assume that the variables are named $$x_1,x_2,$$from left to right. $$\begin{bmatrix}1 & 0 & 5 & 3 & 2\\0 & 1 & -2 & 4 & -7 \\0 & 0 & 1 & 1 & 3\end{bmatrix}$$

emancipezN 2021-06-03 Answered

### Determine whether the statement is true or false. Justify your answer. You cannot write an augmented matrix for a dependent system of linear equations in reduced row-echelon form.

Sinead Mcgee 2021-05-26 Answered

### Refer to the system of linear equations $$\begin{cases}-2x+3y=5\\6x+7y=4\end{cases}$$ Is the augmented matrix row-equivalent to its reduced row-echelon form?

Clifland 2021-05-25 Answered

### Determine whether the following statement is true or false. If the reduced row echelon form of the augmented matrix of a consistent system of mm linear equations in nn variables contains kk nonzero rows, then its general solution contains kk basic variables.

emancipezN 2021-05-23 Answered

### 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. $$\begin{bmatrix}1 & 0 & -2 & | &6\\0 & 1 &3 & | & 1 \end{bmatrix}$$

pedzenekO 2021-05-23 Answered

### 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.

zi2lalZ 2021-05-21 Answered

### Suppose that the augmented matrix for a system of linear equations has been reduced by row operations to the given reduced row echelon form. Solve the system. Assume that the variables are named $$x_1,x_2$$... from left to right. $$\begin{bmatrix}1 & 0&0&-7&8 \\0 & 1&0&3&2 \\0 & 0&1&1&-5 \\ \end{bmatrix}$$

illusiia 2021-05-18 Answered

### Write the vector form of the general solution of the given system of linear equations. $$x_1+3x_2+2x_4=0$$ $$x_3−6x_4=0$$

Efan Halliday 2021-05-18 Answered

### 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. $$\begin{bmatrix}1 & 0&|&3 \\0 & 1&|&-5 \end{bmatrix}$$

pancha3 2021-05-18 Answered

### The row echelon form of a system of linear equations is given. (a)Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or $$x_1,x_2,x_3,x_4$$ as variables. (b)Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. $$\begin{bmatrix}0 & -3&|&-4 \\0 & 1&|&0 \end{bmatrix}$$

ankarskogC 2021-05-16 Answered

### 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 $$x_1,x_2,x_3,x_4$$ as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. ⎡⎣⎢100010430420⎤⎦⎥

Joni Kenny 2021-05-14 Answered

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