Linear Algebra Done Right: Solutions and Examples for Success

College
Algebra
Linear algebra

How do you find the inner product and state whether the vectors are perpendicular given $< 8, 4 > \cdot < 2, 4 >$

iocasq4 2022-01-23

What is the Use for transformations of a matrix?

Elsa Barron 2022-01-23

Discuss the cases of Gaussian elimination method.

Motalli21 2022-01-23

Utilize the Gauss-Jordan elimination method to solve the system of linear equations. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.)
x+2y+z=−4
−2x−3y−z=2
4x+8y+4z=−16

Fiona Petersen 2022-01-23

Let V be a vector space over F. Explain why we can think of V as a vector space over K ( K subset of F)?

estadsocm3 2022-01-23

How do I find the angle between two vectors in three-dimensional space?

Alisha Pitts 2022-01-22

What is the span of a matrix?

Haialarmz6 2022-01-22

How do you determine if the vectors are coplanar: a = [-2,-1,4], b = [5,-2,5], and c = [3,0,-1]?

Trace Cline 2022-01-22

Which of the following statements are true/false?Justify your answer.
(i) $R^{2}$ has infinitely many non-zero, proper vector subspaces.
(ii) Every system of homogeneous linear equations has a non zero solution.

licencegpopc 2022-01-22

How do you find the equation of the plane in xyz-space through the p=(4,5,4) and perpendicular to the n=(−5,−3,−4)?

treslagosnv 2022-01-22

Is there an infinite dimensional vector space H with bounded linear operator from H onto H which preserves the inner product?

dublattm 2022-01-22

Solve the given system of equations, or else show that there is no solution.
a) $x_{1} + 2 x_{2} - x_{3} = 1$
$2 x_{1} + x_{2} + x_{3} = 1$
$x_{1} - x_{2} + 2 x_{3} = 1$
b) $x_{1} + 2 x_{2} - x_{3} = - 2$
$- 2 x_{1} - 4 x_{2} + 2 x_{3} = 4$
$2 x_{1} + 4 x_{2} - 2 x_{3} = - 4$

Kaydence Huff 2022-01-21

Can I exchange column and then use the row transformation when converting a matrix into a row echelon form?
$A = [\begin{array}{cccc} 4 & 2 & 1 & 3 \\ 6 & 3 & 4 & 7 \\ 2 & 1 & 0 & 1 \end{array}]$
1) $C_{3} \leftrightarrow C_{1} [\begin{array}{cccc} 1 & 2 & 4 & 3 \\ 4 & 3 & 6 & 7 \\ 0 & 1 & 2 & 1 \end{array}]$
2) $R_{2} = R_{2} - 4 R_{1} [\begin{array}{cccc} 1 & 2 & 4 & 3 \\ 0 & - 5 & - 10 & - 5 \\ 0 & 1 & 2 & 1 \end{array}]$
$4 - 4 = 0$
$3 - 8 = - 5$
$6 - 16 = - 10$
$7 - 12 = - 5$
3) $R_{3} = R_{3} + \frac{R_{2}}{5} [\begin{matrix} 1 & 2 & 4 & 3 \\ 0 & - 5 & - 10 & - 5 \\ 0 & 0 & 0 & 0 \end{matrix}]$
$1 - 1$
$2 - 2$
$1 - 1$
$∴ l_{(A)} = 2$

Gavin Frye 2022-01-21

How do vectors represent a point in space?

bistandsq 2022-01-21

Find the inverse of the matrix if it exists.
$[\begin{array}{cc} - 7 & 4 \\ 8 & - 5 \end{array}]$

Selena Cowan 2022-01-21

Solve the linear system by Gaussian elimination
$x_{1} + x_{2} + 2 x_{3} = 8$
$- x_{1} \pm 2 x_{2} + 3 x_{3} = 1$
$3 x_{1} + 7 x_{2} + 4 x_{3} = 10$

poveli1e 2022-01-21

Which vectors define the complex number plane?

Caroline Elliott 2022-01-21

Solve the system
$3 x_{1} + 2 x_{2} - x_{3} = 4$
$x_{1} - 2 x_{2} + 2 x_{3} = 1$
$11 x_{1} + 2 x_{2} + x_{3} = 14$

Aaden Lam 2022-01-21

For what value of $λ$ the following vectors will form a basis for $E^{3}$ .
$a_{1} = (1, 5, 3), a_{2} = (4, 0, λ), a_{3} = (1, 0, 0)$ ?

Jay Mckay 2022-01-21

What is the norm or $< - 7, 6, - 1 > ?$

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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