# Linear equation forms questions and answers

Recent questions in Forms of linear equations
Forms of linear equations

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

Forms of linear equations

### The row echelon form of a system of linear equations is given. (a)Writethesystemofequationscorrespondingtothegivenmatrix.Usex,y.or x,y,z.or $$x_1,x_2,x_3,x_4$$ asvariables. (b)Determinewhetherthesystemisconsistentorinconsistent.Ifitisconsistent,givethesolution. $$\begin{bmatrix}1&2&|&5\\0&1&|&-1 \end{bmatrix}$$

Forms of linear equations

### 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. $$\displaystyleλ{1}=-{1}\to{\left\lbrace\begin{array}{cc} {1}&{1}\end{array}\right\rbrace},λ{2}={2}\to{\left\lbrace\begin{array}{cc} {1}&-{1}\end{array}\right\rbrace}$$

Forms of linear equations

### 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. $$\begin{bmatrix}1&-4&5\\0&0&0\\0&0&0 \end{bmatrix}$$

Forms of linear equations

### 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 $$x_1,x_2,…x ,…$$ from left to right. $$\begin{bmatrix}1&0&0&-3 \\0&1&0&0\\0&0&1&7 \end{bmatrix}$$

Forms of linear equations

### A bank loaned out $11,000, part of it at the rate of 7% annual interest, and the rest at 9% annual interest. The total interest earned for both loans was$860.00. How much was loaned at each rate? ___ was loaned at 7% and ___ was loaned at 9%.

Forms of linear equations

### Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations. \left{\begin{array}{c} 7 x-5 y=11 x-y=-5 \end{array}\right.

Forms of linear equations

### Determine whether each first-order differntial equation is separable, linear, both or nether: a) $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}+{e}^{{{x}}}{y}={x}^{{{2}}}{y}^{{{2}}}$$ b) $$\displaystyle{y}+{\sin{{x}}}={x}^{{{3}}}{y}'$$ c) $$\displaystyle{\ln{{x}}}-{x}^{{{2}}}{y}={x}{y}'$$ d) $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}+{\cos{{y}}}={\tan{{x}}}$$

Forms of linear equations

### 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. [1−32040\000001\000000]

Forms of linear equations

### 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. $$\displaystyleλ{1}={1}\to{\left\lbrace\begin{array}{cc} {2}&{1}\end{array}\right\rbrace},λ{2}={3}\to{\left\lbrace\begin{array}{cc} {3}&{1}\end{array}\right\rbrace}$$

Forms of linear equations

### 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. [10−6\013\000]

Forms of linear equations

### 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. [ 1 0 0 −1 0 1 0 3 0 0 1 4 0 0 0 0 ]

Forms of linear equations

### Write the vector form of the general solution of the given system of linear equations. x1+3x2+2x4=0 x3−6x4=0

Forms of linear equations

### 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. [103024][

Forms of linear equations

### Write the vector form of the general solution of the given system of linear equations. x1+2x2−x3+x4=0

Forms of linear equations

### Reduce the system of linear equations to upper triangular form and solve. x−2y=2 4y−2x=−4 ​

Forms of linear equations

### Let AX = B be a system of linear equations, where A is an m×nm×n matrix, X is an n-vector, and BB is an m-vector. Assume that there is one solution X=X0. Show that every solution is of the form X0+Y, where Y is a solution of the homogeneous system AY = O, and conversely any vector of the form X0+Y is a solution.

Forms of linear equations

### Find the linearization L(x) of the function at a. $$\displaystyle{f{{\left({x}\right)}}}={x}^{{4}}\mp{3}{x}^{{2}}$$, $$\displaystyle{a}=-{1}$$

Forms of linear equations