Linear Algebra Done Right: Solutions and Examples for Success

College
Algebra
Linear algebra

An object moving in the xy-plane is acted on by a conservative force described by the potential energy function $U (x, y) = α (\frac{1}{x^{2}} + \frac{1}{y^{2}})$ where $α$ is a positive constant. Derivative an expression for the force expressed terms of the unit vectors $\vec{i}$ and $\vec{j}$ .

Oswaldo Riley 2023-03-31

I need to find a unique description of Nul A, namely by listing the vectors that measure the null space
$A = [\begin{matrix} 1 & 5 & - 4 & - 3 & 1 \\ 0 & 1 & - 2 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{matrix}]$
?

Aron Campbell 2023-03-30

T must be a linear transformation, we assume. Can u find the T standard matrix. $T : R^{2} \to R^{4}, T (e_{1}) = (3, 1, 3, 1) and T (e_{2}) = (- 5, 2, 0, 0), w h e r e e_{1} = (1, 0) and e_{2} = (0, 1)$
?

Jacoby Blevins 2023-03-30

Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and area of the triangle PQR
Consider the points below
P(1,0,1) , Q(-2,1,4) , R(7,2,7).
a) Find a nonzero vector orthogonal to the plane through the points P,Q and R.
b) Find the area of the triangle PQR.

atentan4t9j 2023-03-25

Consider two vectors A=3i - 1j and B = - i - 5j, how do you calculate A - B?

Kira Yoder 2023-03-23

What is the dot product of $< 1, - 4, 5 >$ and $< - 5, 7, 3 >$ ?

Oswaldo Riley 2023-03-23

Let vectors A=(1,0,-3) ,B=(-2,5,1) and C=(3,1,1), how do you calculate 2A-3(B-C)?

miljanwpd2 2023-03-23

What is the projection of $< 6, 5, 3 >$ onto $< 2, - 1, 8 >$ ?

Arturo Callahan 2023-03-18

Which of the following is not a vector quantity?
A)Weight;
B)Nuclear spin;
C)Momentum;
D)Potential energy

Marisa Singleton 2023-03-17

How to find all unit vectors normal to the plane which contains the points $(0, 1, 1), (1, - 1, 0)$ , and $(1, 0, 2)$ ?

Isis Everett 2023-03-16

How to find unit vector perpendicular to plane: 6x-2y+3z+8=0?

Kai Kerr 2023-03-13

Can we say that a zero matrix is invertible?

Autumn Hebert 2023-03-12

How do I find the sum of three vectors?

umatisi6ar 2023-03-11

How to find done in moving a particle P (0,0) to Q(4,7) if the magnitude and direction of the force is given by $v = < 1, 4 >$ ?

Beau Mckee 2023-03-11

How do I find the vertical component of a vector?

Bruno Schneider 2023-03-11

How would you find a unit vector perpendicular to plane ABC where points are A(3,-1,2), B(1,-1,-3) and C(4,-3,1)?

pwysi85o 2023-03-11

What does determinant of $0$ mean?

Karlee Rivas 2023-03-09

What is the value of $(A$ x $B)^{2}$ + ${(A \cdot B)}^{2}$ ?

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.

Linear algebra