Linear Algebra Done Right: Solutions and Examples for Success

College
Algebra
Linear algebra

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%.

Tammy Todd 2021-09-21

Find a unit vector that has the same direction as the given vector. 8i-j+4k

ruigE 2021-09-21

An idealized velocity field is given by the formula $V = 4 t ξ - 2 t^{2} y j + 4 x z k$ Is this flow field steady or unsteady? Is it two or three dimensional? At the point $(x, y, z) = (- 1, 1, 0)$ , compute (a) the acceleration vector.

pedzenekO 2021-09-20

Check to see if each first-order differential equation is linear, separable, both, or neither:
a) $\frac{d y}{d x} + e^{x} y = x^{2} y^{2}$
b) $y + \sin x = x^{3} y^{'}$
c) $\ln x - x^{2} y = x y^{'}$
d) $\frac{d y}{d x} + \cos y = \tan x$

ka1leE 2021-09-20

Use the definition of Ax to write the matrix equation as a vector equation, or vice versa.
$[\begin{matrix} 7 & - 3 \\ 2 & 1 \\ 9 & - 6 \\ - 3 & 2 \end{matrix}] [\begin{matrix} - 2 \\ - 5 \end{matrix}] = [\begin{matrix} 1 \\ - 9 \\ 12 \\ - 4 \end{matrix}]$

necessaryh 2021-09-20

Consider the $3 \times 3$ matrices with real entrices. Show that the matrix forms a vector space over R with respect to matrix addition and matrix multiplication by scalars?

Alyce Wilkinson 2021-09-20

Differentiate.
$f (θ) = θ \cos θ \sin θ$

nicekikah 2021-09-20

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. $[\begin{matrix} 1 & - 3 & 2 & 0 & 4 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{matrix}]$

CMIIh 2021-09-20

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.
$λ 1 = 1 \to {\begin{array}{cc} 2 & 1 \end{array}}, λ 2 = 3 \to {\begin{array}{cc} 3 & 1 \end{array}}$

Khaleesi Herbert 2021-09-20

Vector Cross Product
Let vectors A=(1,0,-3), B =(-2,5,1), and C =(3,1,1). Calculate the following, expressing your answers as ordered triples (three comma-separated numbers).
(C) $(2 \overset{―}{B}) (3 \overset{―}{C})$
(D) $(\overset{―}{B}) (\overset{―}{C})$
(E) $o v e r \to A (o v e r \to B \times o v e r \to C)$
(F)If ${\overset{―}{v}}_{1} and {\overset{―}{v}}_{2}$ are perpendicular, $| {\overset{―}{v}}_{1} \times {\overset{―}{v}}_{2} |$
(G) If ${\overset{―}{v}}_{1} and {\overset{―}{v}}_{2}$ are parallel, $| {\overset{―}{v}}_{1} \times {\overset{―}{v}}_{2} |$

remolatg 2021-09-19

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

Chardonnay Felix 2021-09-19

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

bobbie71G 2021-09-19

Find the scalar and vector projections of b onto a.
$a = i + j + k, b = i - j + k$

sjeikdom0 2021-09-18

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

hexacordoK 2021-09-18

Соnstruct a nonzerо $3 \times 3$ matriх А and a nonzerа vector b such that b is in Nul A.

ka1leE 2021-09-18

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

Trent Carpenter 2021-09-18

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

Tammy Todd 2021-09-18

List five vectors in Span ${v_{1}, v_{2}}$ . For each vector, show the weights on $v_{1}$ and $v_{2}$ used to generate the vector and list three entries of the vector. Do not make a seketch.
$v_{1} = [\begin{matrix} 7 \\ 1 \\ - 6 \end{matrix}], v_{2} = [\begin{matrix} - 5 \\ 3 \\ 0 \end{matrix}]$

lwfrgin 2021-09-18

Find $| u \cdot v |$ and determine whether $u \cdot v$
is directed into the screen or out of the screen.
$| u \cdot v | = ? ?$

Emeli Hagan 2021-09-18

Find, correct to the nearest degree, the three angles of the triangle with the given vertices. P(2, 0), Q(0, 3), R(3, 4)

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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