Linear Algebra Done Right: Solutions and Examples for Success

College
Algebra
Linear algebra

How do you convert (−2,5) to polar form?

Arlene Julia Torregue Gueta2022-08-29

Determine whether the set S spans R2. If the set does not span give a geometric description of the subspace that it does span.
1. S = { (2, 1), (-1, 2) }

2. S = { (1, 3), (-2, -6), (4, 12)}

3. S = { (-3, 5) }

4. S = { (5, 0), (5, -4) }

5. S = { (-1, 2), (2, -4) }

Miriam Mekhail2022-08-28

Construct a graph corresponding to the linear equation y=2x−6 $y = 2 x - 6$ .

Amy Dover2022-08-24

Assume that a family is purchasing a typical house by making a $30,000 down payment and then financing a $250,000 mortgage at an annual interest rate of 4.25% (a typical rate for a 30-year loan). The size of their monthly payment will depend on the term of the mortgage.
The formula or the Excel function “pmt” can be used to compute these monthly mortgage payments. If using Excel the 3 arguments of function “pmt” are:
Rate (the monthly interest rate): 0.0425/12
Nper (the total number of monthly payments) and
Pv (the mortgage amount)

Find the monthly payments if the $250,000 was financed over 15 years.
Find the monthly payments if the $250,000 was financed over 30 years.
Multiply your answer to part (a) by the number of payments to find how much the family would need to pay in total over the life of the 15-year loan. Subtract the principal amount from this to give the amount of interest paid over the life of the loan.
Multiply your answer to part (b) by the number of payments to find how much the family would need to pay in total over the life of the 30-year loan. Subtract the principal amount from this to give the amount of interest paid over the life of the loan.
A standard rule for lenders is that a family’s house payment should not exceed 28% of their monthly income. For a family making $5500 per month, this would equate to $1540 per month. Assuming monthly costs of $250 for property tax and homeowner’s insurance, this would allow for a $1290 monthly mortgage payment.
The formula or the Excel function “pv” can be used to compute the mortgage a family could afford. If using Excel the 3 arguments of function “pv” are:
Rate (the monthly interest rate): 0.0425/12
Nper (the total number of monthly payments) and
Pmt (the monthly mortgage amount)

Assuming that a family wants to make a $1290 monthly payment, give the mortgage that a family could afford at an annual interest rate 4.25% for a 15-year mortgage.
Assuming that a family wants to make a $1290 monthly payment, give the mortgage that a family could afford at an annual interest rate 4.25% for a 30-year mortgage.

X-1^3=0

FIRE YEDENE2022-08-17

Find the parametric and symmetric equations of the line L that passes through the Point (2, −4, 8) and parallel to v = 〈1, 2, −2〉.

pominjaneh6 2022-08-14

1) Craig is saving to buy a vacation home. He inherits some money from a wealthy uncle, then combines this with the $28,000 he has already saved and doubles the total in a lucky investment. He ends up with $116,000-Just enough to buy a cabin on the lake. How much did he inherit?
2) Solve the nonlinear inequality. Express the solution using interval notation. x^3-64x > 0

Endiyah Neal2022-08-12

Which expression consists of exactly two terms when simplified?
(7 + 3)x
(7 + 3), x
11(x + 7)
11(, x, + 7)
12x + 5(y + 8)
12, x, + 5(, y, + 8)
(3x + 8y ) + 4z

Ashlynn Hale 2022-08-10

An augmented matrix of a system of equations has been transformed by row operations into the 3 equations in 3 variables matrix below. State the solution to this system as (x,y,z) Enter your answer as an ordered triple within parenthesis separated by commas (x,y,z). Avoid entering spaces and decimal points Use fractions if relevant.
$[\begin{matrix} 1 & 0 & 0 & ⋮ & - 3 \\ 0 & 1 & 0 & ⋮ & \frac{2}{3} \\ 0 & 0 & 1 & ⋮ & \frac{1}{4} \end{matrix}]$

Bobby Mitchell 2022-08-07

Show that the plane that passes through the three points
A=(a1,a2,a3)
B=(b1,b2,b3)
C=(c1,c2,c3)
consists of the points P=(x,y,z) given by
$| \begin{matrix} a_{1} - x & a_{2} - y & a_{3} - z \\ b_{1} - x & b_{2} - y & b_{3} - z \\ c_{1} - x & c_{2} - y & c_{3} - z \end{matrix} |$

tamkieuqf 2022-08-05

Find 2 unit vectors orthogonal to both i+j+k and 2i+k

proximumha 2022-08-05

Express the vector v as the sum of a vector parallel to b and a vector orthogonal to b.
v = 4i - 2j + 6k, b= -2i+j-3k

erkentrs 2022-08-05

Express the vector v as the sum of a vector parallel to b anda vector orthogonal to b.
v = 4i -2j +6k
b= -2i + j -3k

cofak48 2022-08-04

Let $A = [\begin{matrix} 3 & 2 \\ 5 & 3 \end{matrix}]$ and $B = [\begin{matrix} - 7 & 9 \\ 1 & - 9 \end{matrix}]$
Find 3A-2B.

Gorlandint 2022-08-02

Perform the indicated matrix operation.
$[\begin{matrix} 2 x + y & x - 2 y & 4 x \\ 3 x & 3 y & x + y \end{matrix}] + [\begin{matrix} 5 x & 8 y & 3 x + y \\ 5 x + 5 y & x & 2 x \end{matrix}]$

Roselyn Daniel 2022-08-01

Determine if there is a plane in $R^{3}$ which contains both lines $l_{1} a n d l_{2}$ where: $l_{1} : x = 2 t + 3, y = t + 3, z = 3 t + 8$ and $l_{2} : x = 3 s - 2, y = 3 s - 1$ , and z = 4s+1.

Ishaan Booker 2022-08-01

Let a be the two dimensional vector <-2, 4>
Consider a general vector $b \neq 0$ whose position vector makes an angle $θ$ withthe x-axis.
Explain why, no matter what b is, the tip of the positionvector of $\frac{b}{| b |}$ is on the unit circle.

Spoorthi 2022-07-31

Let T be the linear transformation whose standard matrix is given below. A=[7 5 4 -9 ,10 6 16 -4 ,12 8 12 7, -8 -6 -2 5] a) Decide if T is a one-to-one mapping.
b)Decide if Rn is mapped onto Rm

Damien Horton 2022-07-31

Find the inverse of the following matrix A, if possible. Check that $A A^{- 1} = I$ and $A^{- 1} A = I$
$A = [\begin{matrix} 7 & 4 \\ 7 & 7 \end{matrix}]$
The inverse, $A^{- 1}$ is ?

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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