Linear Algebra

Welcome to the Linear Algebra category on Questions LLC! Whether you are a struggling student in need of assistance or a curious individual looking to explore the world of mathematical transformations, this category is a haven for all things related to Linear Algebra. From matrices and vectors to systems of linear equations and eigenvalues, our community of knowledgeable experts and enthusiastic enthusiasts is here to help unravel the complexities of this fundamental branch of mathematics. Don't hesitate to dive into the questions and answers, or feel free to pose your own inquiries to further expand your understanding of Linear Algebra.

Questions (897)

Which of these graphs shows that the linear system −2x + y = 6 and 4x − 2y = −12 has an infinite number of solutions?
1. 1 answer
2. asked by here to help
3. 106 views
Given vectors u=(-6,4) and v=(3,3), determine if the vectors are orthogonal. if they are not orthogonal, find the angle between
1. 7 answers
2. asked by T
3. 2,022 views
For a vector $\bold{v}$, let $\bold{r}$ be the reflection of $\bold{v}$ over the line\[\bold{x} = t \begin{pmatrix} 2 \\ -1
1. 4 answers
2. asked by Bob
3. 1,389 views
Find the $2 \times 2$ matrix $\bold{A}$ such that\[\bold{A} \begin{pmatrix} 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2
1. 5 answers
2. asked by Zheng
3. 3,236 views
Find the entries of the following matrices:(a) the 2 ×2 matrix M for the reflection across the line y = x. (b) the 2 ×2 matrix
1. 5 answers
2. asked by Eunice
3. 2,185 views
Which value of k will make the plane r=(k,3k,12) +s(2,2,3)+t(-1,1,3), s,teR passing through the origin?a) 2 b) 1 c)0 d) -1
1. 4 answers
2. asked by Jenny
3. 1,955 views
Any ideas on how to solve this: Use a vector solution to show that a scalar equation for the line through the points P1(x1, y1)
1. 3 answers
2. asked by Derek
3. 827 views
How do we know the ith of an invertible matrix B is orthogonal to the jth column of B^-1 , if i is not equal/unequal to j?
1. 4 answers
2. asked by Nolan
3. 2,347 views
Compute the distance between the parallel lines given by\[\begin{pmatrix} 1 \\ 4 \end{pmatrix} + t \begin{pmatrix} 4 \\ 3
1. 4 answers
2. asked by Zheng
3. 1,125 views
Consider the following system of linear equations:2x1+2x2+4x3 = −12 x1+6x2−8x3 = −6 x1−2x2+9x3 = −8 Let A be the
1. 4 answers
2. asked by sal
3. 1,598 views
Find all vectors v in 2 dimensions having ||v ||=5 where the i -component of v is 3ivectors:
1. 4 answers
2. asked by George
3. 4,792 views
1. What is the solution of the matrix equation?|9 4| |-9 -6| | | X =| | |2 1| |-1 -8| A.) |5 -26| |9 -60| B.) |-5 26| |-1 -8|
1. 7 answers
2. asked by Cassie
3. 1,855 views
given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q are the unit vectors,find the dot product of vectors p
1. 3 answers
2. asked by bhawani
3. 1,505 views
Let W be the subspace of R5 spanned by the vectors w1, w2, w3, w4, w5, wherew1 = 2 −1 1 2 0 , w2 = 1 2 0 1 −2 , w3 = 4 3 1 4
1. 4 answers
2. asked by sara
3. 2,386 views
what is the basis of a subspace or R3 defined by the equation2x1+3x2+x3=0 I know the basis is vectors <-3,2,0> and <-1,0,2> but
1. 4 answers
2. asked by jen
3. 5,799 views
do vectors have an x component of zero?
1. 4 answers
2. asked by k
3. 4,293 views
Hi! I need help with these two questions. Thanks! :)1.) Can we multiply the Matrix A (which is 3 x 4 matrix) by the other
1. 3 answers
2. asked by Emily
3. 753 views
describe the transformation from LAP to L'A'P
1. 1 answer
2. asked anonymously
3. 19 views
Matrices Quick Check5 of 55 of 5 Items Question Which statement correctly describes the matrix? R=[428101580495] (1 point)
1. 1 answer
2. asked anonymously
3. 56 views
Question B=[212] (1 point) Matrix B has the dimensions ?×?.
1. 1 answer
2. asked anonymously
3. 14 views
Question Recognize which statement correctly describes the matrix. L=⎡⎣⎢135297⎤⎦⎥ (1 point) Responses Matrix L has
1. 1 answer
2. asked anonymously
3. 33 views
Which statement correctly describes the matrix?
1. 1 answer
2. asked anonymously
3. 22 views
Recognize which statement correctly describes the matrix.L=⎡⎣⎢135297⎤⎦⎥ (1 point) Responses Matrix L has the
1. 1 answer
2. asked anonymously
3. 69 views
Operations with Matrices Quick Check2 of 52 of 5 Items Question Subtract the matrices. Which response is the difference in the
1. 1 answer
2. asked anonymously
3. 54 views
Subtract the matrices. Which response is the difference in the values in the first row, second column?[392515281921]−[24162322
1. 1 answer
2. asked anonymously
3. 17 views
Multiply the matrix by the scalar 0.25. Find the element in the first row, second column of the answer.[2016−12−24] (1
1. 1 answer
2. asked anonymously
3. 40 views
Multiply the following matrix with the given scalar. (1 point)3 {9 8} {10 4} {6 5} ANSWER [27 20] [30 12] [18 20] [12 11] [13 7]
1. 3 answers
2. asked by local.trin
3. 13 views
Find conditions on k that will make the matrix A invertible. To enter your answer, first select 'always', 'never', or whether k
1. 4 answers
2. asked by sal
3. 4,167 views
Use Cramer's rule to solveX1-5x2-2x3=-2 2x1+3x3=11 4x1+x2-x3=1
1. 2 answers
2. asked by SEIFU ABERRA
3. 100 views
Find two vectors perpendicular to both (3, -6, 3) and (-2, 4, 2).
1. 7 answers
2. asked by vectors
3. 71 views
Find a non zero- vector orthogonal to (1, 2, -1)
1. 1 answer
2. asked by asfaw
3. 82 views
Find a vector r(t) = at^2 + bt + c such that the set B = {2t + 1, t^2 - 1, r(t)} is a basis for P2.Find the values of a, b, c
1. 1 answer
2. asked by Beth
3. 223 views
Let A be the matrix below and define a transformation T:ℝ3→ℝ3 by T(U) = AU. For the vector B below, find a vector U such
1. 3 answers
2. asked by sal
3. 2,598 views
Let L be the line with parametric equationsx = −4+2t y = 8+t z = 8+3t Find the vector equation for a line that passes through
1. 3 answers
2. asked by Big L's
3. 587 views
The matrix;[ 1 -2 0] [-2 -1 1] [ 0 0 -1] I have found the eigenvalues to be -1 and +/- 5^1/2 but am having problems putting the
1. 1 answer
2. asked by Rom
3. 429 views
Prove that the trace is a similarity invariant.In other words, if two matrices are similar, then they must have the same trace.
1. 1 answer
2. asked by mathstudent
3. 661 views
write the system of equations represented by the matrix[0 1 2 4] [-2 3 6 9] [1 0 1 3] a: x+2y=4 -2x-3y+69=0 x+y=3 b: x+2y=4
1. 10 answers
2. asked by mia
3. 6,625 views
If det(A)=-7A= | a b c | | d e f | | g h i | Find det(2A^-1), det((2A)^-1). Find | a g d | | b h e | | c i f |
1. 3 answers
2. asked by Amelie
3. 943 views
I am so confused with this last part of the unit! What in the world is going on: Use normal vectors to determine the
1. 4 answers
2. asked by Derek
3. 1,500 views
If vector u = (5, 3) and vector v = (-1, 4), what is the component form of vector u + v?
1. 3 answers
2. asked anonymously
3. 83 views
Determine two unit vectors that are perpendicular to both a=[-5,6,2] and d=[3,3,-8].
1. 2 answers
2. asked by Anonymous
3. 594 views
For any two vectors u and v show that(u.v)^2-[(u.v)×v].u = u^2v^2
1. 1 answer
2. asked by gourav
3. 356 views
How do you create a rotation matrix that will represent a rotation of angle theta about a vector (x,y,z)?This is instead of
1. 1 answer
2. asked by Mike
3. 1,015 views
Matrix Algebra AssignmentLet A= 4 −1 6 9 and B= 0 3 3 −2 Find: 1. A + B 2. AB 3. BA 4. A' (the transpose of A). 5. What is
1. 1 answer
2. asked by Shavon
3. 401 views
clockwise rotation matrix example
1. 7 answers
2. asked anonymously
3. 58 views
Consider the linear transformation T: R^3->R^3 which acts by rotation around the y-axis by an angle of pi, followed by a shear
1. 1 answer
2. asked by Brody
3. 628 views
11product AB of the two matricesA= 1 2 3 4 And B= 1 2 3 4
1. 2 answers
2. asked anonymously
3. 55 views
Let T:R3 →R 3 be a linear transformation such that T(1,0,0)=(2,−1,4),T(0,1,0)=(1,−2,3), and T(0,0,1)=(2,−2,0). Find the
1. 2 answers
2. asked anonymously
3. 52 views
Using a row operation, compute the inverse of the matrix A= ( 1 1 10 2 3 5 5 1)
1. 2 answers
2. asked by Joseph Anyanwu
3. 92 views
Find the unique solutions for the systems of linear equationsw+2x+2y-z=5 2w-x-y+4z=5 -w+3x+4y-2z=5 3w+x+y-4z=4
1. 2 answers
2. asked by Joseph Anyanwu
3. 90 views

Linear Algebra

Pages