Linear Algebra Done Right: Solutions and Examples for Success

College
Algebra
Linear algebra

Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked is an exponential random variable with mean 20. Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the car, what is the probability that she would get at least 20,000 additional miles out of it? Repeat under the assumption that the lifetime mileage of the car is not exponentially distributed, but rather is (in thousands of miles) uniformly distributed over (0, 40).

cleritere39 2021-11-16

Write the system first as a vector equation and then as a matrix equation.
$8 x_{1} - x_{2} = 4$
$5 x_{1} + 4 x_{2} = 1$
$x_{1} - 3 x_{2} = 2$

kolonelyf4 2021-11-16

Find all x in $R^{4}$ that are mapped into the zero vector by the transformation $X \mapsto A X$ for the given matrix A.
$A = [\begin{matrix} 1 & 3 & 9 & 2 \\ 1 & 0 & 3 & - 4 \\ 0 & 1 & 2 & 3 \\ - 2 & 3 & 0 & 5 \end{matrix}]$

sklicatias 2021-11-16

Find the coordinate vector of w relative to the basis $S = {u_{1}, u_{2}} f o r R^{2} u_{1} = (1, - 1), u_{2} = (1, 1); w = (1, 0)$

signokodo7h 2021-11-15

Find the area of triangle PQR, P(0,-2,0), Q(4,1,-2), R(5,3,1)

actever6a 2021-11-14

Identify the surface with the given vector equation.
$r (s, t) = < s, t, t^{2} - s^{2} >$

katelineliseua 2021-11-13

The three components of velocity in a flow field are given by
$u = x^{2} + y^{2} + z^{2}$
$v = x y + y z + z^{2}$
$w = - 3 x z - \frac{z^{2}}{2} + 4$
(a) Determine the volumetric dilatation rate and interpret the results. (b) Determine an expression for the rotation vector. Is this an irrotational flow field?

rabbitz42z8 2021-11-13

I'm having trouble with these types of questions. I have the following vector $u = (4, 7, - 9)$ and it wants me to find 2 vectors that are perpendicular to this one.
I know that $(4, 7, - 9) \cdot (x, y, z) = 0$

rastafarral6 2021-11-13

Hi i know this is a really really simple question but it has me confused.
I want to calculate the cross product of two vectors
$\vec{a} \times \vec{r}$
The vectors are given by
$\vec{a} = a \vec{z}, \vec{r} = x \vec{x} + y \vec{y} + z \vec{z}$
The vector $\vec{r}$ is the radius vector in cartesian coordinares.
I want to calculate the cross product in cylindrical coordinates, so I need to write $\vec{r}$ in this coordinate system.
The cross product in cartesian coordinates is
$\vec{a} \times \vec{r} = - a y \vec{x} + a x \vec{y}$ ,
however how can we do this in cylindrical coordinates?

trainart1 2021-11-13

Find the derivative of the vector function. $r (t) = a + t b + t^{2} c$

sputavanomr 2021-11-13

Find the curvature of $r (t) = < 9 t, t^{2}, t^{3} >$ at the point (9, 1, 1).

(P^~Q)^(P→Q)

check whether it is in contradiction form or not.

Mahagnazk 2021-11-11

Describe the vector space's zero vector (the additive identity).
$R^{4}$

klytamnestra9a 2021-11-11

Find a vector equation and parametric equations for the line.
The line through the point $(1, 0, 8)$ and perpendicular to the plane $x + 3 y + z = 3$

Lewis Harvey 2021-11-05

Find an explicit description off Nul A by listing vectors that span the null space.
$A = [\begin{matrix} 1 & 3 & 5 & 0 \\ 0 & 1 & 4 & - 2 \end{matrix}]$

استخدم قاعدة السلسلة لإيجاد المشتقات الجزئية المشار إليها.

N =

ص + ف

ص + ص

، p = u + vw ، q = v + uw ، r = w + uv ؛

∂N

∂u

و

∂N

∂v

و

∂N

∂w

عندما u = 3 ، v = 5 ، w = 6

∂N

∂u

=
7486

∂N

∂v

=

∂N

∂w

=

Suppose f is a differentiable function of x and y, and

g(r, s) = f(2r − s, s2 − 7r).

Use the table of values below to calculate

gr(4, 3)

and

gs(4, 3).

  f     g     fx     fy

  (5, −19)

4

9

7

1

  (4, 3)

9

4

5

2

gr(4, 3) =

gs(4, 3) =
Suppose f is a differentiable function of x and y, and
g(r, s) = f(2r − s, s2 − 7r).
Use the table of values below to calculate
gr(4, 3)
and
gs(4, 3).

  f     g     fx     fy

  (5, −19)

4

9

7

1

  (4, 3)

9

4

5

2

gr(4, 3) =

gs(4, 3) =
Suppose f is a differentiable function of x and y, and
g(r, s) = f(2r − s, s2 − 7r).
Use the table of values below to calculate
gr(4, 3)
and
gs(4, 3).

  f     g     fx     fy

  (5, −19)

4

9

7

1

  (4, 3)

9

4

5

2

gr(4, 3) =

gs(4, 3) =

Consider the following.

z = x2 + y2,   x = 5s + 6t,   y = s + t

Find

∂z

∂s

and

∂z

∂t

by using the chain rule. (Enter your answers in terms of s and t.)

∂z

∂s

=

52`s`+62`t`

∂z

∂t

=

62`s`+74`t`

Find

∂z

∂s

and

∂z

∂t

by first substituting the expressions for x and y to write z as a function of s and t. (Enter your answers in terms of s and t.)

∂z

∂s

=

∂z

∂t

=

Do your answers for

∂z

∂s

agree?

YesNo

Do your answers for

∂z

∂t

agree?

YesNo

Use the chain rule to find

∂z

∂s

and

∂z

∂t

.

z = tan−1(x6 + y6), x = s ln(t), y = tes

∂z

∂s

=

∂z

∂t

=

(a)

Find the point at which the given lines intersect.

r =

2, 3, 0

+ t

3, −3, 2

r =

5, 0, 2

+ s

−3, 3, 0

(x, y, z) =

(b)

Find an equation of the plane that contains these lines.

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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