Linear Algebra Done Right: Solutions and Examples for Success

College
Algebra
Linear algebra

Solve the rate of change of f at P in the direction of the vector u. $f (x, y, z) = y^{2} e^{x} y z, P (0, 1, - 1), u = < \frac{3}{13}, \frac{4}{13}, \frac{12}{13} >$

Reeves 2021-09-13

Find an equation of the plane. The plane through the origin and perpendicular to the vector <1, -2, 5>

djeljenike 2021-09-13

Suppose that A is row equivalent to B. Find bases for the null space of A and the column space of A.
$A = [\begin{matrix} 1 & 2 & - 5 & 11 & - 3 \\ 2 & 4 & - 5 & 15 & 2 \\ 1 & 2 & 0 & 4 & 5 \\ 3 & 6 & - 5 & 19 & - 2 \end{matrix}]$
$B = [\begin{matrix} 1 & 2 & 0 & 4 & 5 \\ 0 & 0 & 5 & - 7 & 8 \\ 0 & 0 & 0 & 0 & - 9 \\ 0 & 0 & 0 & 0 & 0 \end{matrix}]$

Maiclubk 2021-09-13

Show that if $A^{2}$ is the zero matrix, then the only eigenvalue of A is 0.

Khadija Wells 2021-09-13

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. $[\begin{matrix} 1 & 0 & 0 & - 3 & 0 \\ 0 & 1 & 0 & - 4 & 0 \\ 0 & 0 & 1 & 5 & 0 \end{matrix}]$

Chardonnay Felix 2021-09-13

Reduce the system of linear equations to upper triangular form and solve.
7x−y=4
3x+2y=1

Tolnaio 2021-09-13

Find the distance between the given parallel planes. 2x-3y+z=4, 4x-6y+2z=3

Cheyanne Leigh 2021-09-07

Vectors u and v are orthogonal. If u=<3, 1+b> and v=<5, 1-b> find all possible values for b.

fortdefruitI 2021-09-07

Find $(t), N (t), a_{T}, and a_{N}$ at the given time t for the plane curver r(t). $r (t) = t^{2} i + 2 t j, t = 1$

cistG 2021-09-05

The average height of a 2 year old boy is 38 inches. an 8 year old averages 56 inches. Use this information to write a linear equation that models the height (in inches), y, in terms of the age (in years), x. Use the linear equation to predict the average height of a 5 year-old boy.

djeljenike 2021-08-30

Find the minimum and maximum values of $y = \sqrt{6} θ - \sqrt{3} \sec θ$
on the interval $[0, \frac{pi}{3}]$

Chardonnay Felix 2021-08-16

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. or 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.
$[\begin{matrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 2 \\ 0 & 0 & 1 & 2 & 3 \end{matrix}]$

hexacordoK 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.

CheemnCatelvew 2021-08-13

Write the vector form of the general solution of the given system of linear equations. $- x_{1} + 2 x_{3} - 5 x_{4} + x_{5} - x_{6} = 0$

preprekomW 2021-08-12

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. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution.
$[\begin{matrix} 1 & 2 & - 1 & 0 \\ 0 & 1 & - 1 & 1 \\ 0 & 0 & 0 & 2 \end{matrix}]$

glamrockqueen7 2021-08-11

Solve the following systems of inequalities graphically on the set of axes below.The state the following coordinates of a point in the solution say
$y \leq x + 6$
$y ≻ \frac{3}{2} x - 4$

Brittney Lord 2021-08-11

Write the vector form of the general solution of the given system of linear equations. $x_{1} + 2 x_{2} - x_{3} + 2 x_{5} - x_{6} = 0$

Ava-May Nelson 2021-08-11

The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution. $[\begin{matrix} 1 & 0 & - 1 & - 2 & - 3 & 1 \\ 0 & 1 & 2 & 3 & 4 & 0 \end{matrix}]$

Yasmin 2021-08-10

The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution. $[\begin{matrix} 1 & 0 & - 1 & - 2 & - 3 & 0 \\ 0 & 1 & 2 & 3 & 4 & 0 \end{matrix}]$

pancha3 2021-08-10

Consider the following system.
${\begin{cases} y = 30 - x \\ 2 y = - x^{2} + 16 x - 12 \end{cases}$

Finding detailed linear algebra problems and solutions has always been difficult because the textbooks would never provide anything that would be sufficient. Since it is used not only by engineering students but by anyone who has to work with specific calculations, we have provided you with a plethora of questions and answers in their original form. It will help you to see some logic as you are solving complex numbers and understand the basic concepts of linear Algebra in a clearer way. If you need additional help or would like to connect several solutions, compare more than one solution as you approach your task.

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