1,954 Answered Questions for the topic linear algebra
03/12/20
Vectors and Span: True or False
(a) The inverse of a rotation matrix [R^θ] is [R^−θ].(b) If the vectors v1, v2, . . ., v3 are such that no two of these vectors are scalar multiples of each other then they must form a linearly...
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Vector Sets and Span
For each set of vectors, determine whether their span is {0}, a line, a plane, all of R2, or all of R3.A) {(0, 0), (3, 7)}B) {(1, 2),(3, 4)}C) {(0, 1, −2),(2, 1, 0),(1, 1, −1)}
Determine which of the following vector sets are and aren't in subspaces
A) The graph of the function y = 4x - 2 in R2B) The graph of the function y = cos(x) - 1 in R2C) The set of solutions (x, y, z) in the equation 3x - 4y + 2z = 0D) The set {(x, y) ∈ R2 : x ≥ 0 and y...
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Inverse Matrix Question
Suppose X and Y are both invertible matrices, and W is a block matrix:
W = [ X Z ]
[ 0 Y ]
Show that W is invertible, and its inverse is:[ X-1 -X-1ZY-1 ] = W-1[ 0 Y -1 ]
Finding the Inverse of a Matrix
Suppose x ∈ R.Find the inverse of the following matrix:
A = [ 1 1 1 ]
[ 0 1 1 ]
[ x 0 1 ]
03/04/20
Row Equivalent Matrices
Determine whether or not the two matrices are row equivalent:
matrix one:
[ 1 2 1 ]
[ 1 -1 1 ]
[ 2 1 2 ]
matrix two:
[ 0 -2 0 ]
[ 1 1 1 ]
[ 1 0 1 ]
03/04/20
Inverse Matrices
Find the inverse of the following matrices if it exists:
1.
[ 1 -2 ]
[ -3 5 ]
2.
[ -2 0 2 ]
[ 4 -2 -1 ]
[ 0 2 -2 ]
Linear Algebra Reduced Row Echelon Form
03/04/20
Reduced Row Echelon Form
Compute the reduced row echelon form of each of the follow matrices:
(a)
[ 2 1 ]
[ -3 -2 ]
(b)
[ 3 -3 -3 ]
[ 2 -3 -4 ]
(c)
[ 2 2 ]
[ 3 0 ]
[ 1 0 ]
(d)
[ 1 -2 0 ]
[ -2 4 -1 ]
[ 2 -4 -1 ]
Linear Algebra
03/03/20
If u = (1, 4, 2), v = (3, 5, 6) and w = (2, 2, 3) are three vectors in R3, then (u + v) . 5(u - w) is_____
If u = (1, 4, 2), v = (3, 5, 6) and w = (2, 2, 3) are three vectors in R3, then (u + v) . 5(u - w) is_____
Linear Algebra
03/03/20
If v= (2, 4, 4) and ‖ k v ‖ = 24, then the value of k is:
If v= (2, 4, 4) and ‖ k v ‖ = 24, then the value of k is:
Linear Algebra
03/03/20
Linear Equations in 2 variables
Hi, this is the question that has me stumped the most. Solve for X and Y1/2x + 1/1 = 1y = 15/21x +1/9y = 67/9I believe the answer has no solution but I wanted to hear from you all.
Linear Algebra
03/02/20
A=a+b+c/3 to solve for b in this formula, the first step is to
Linear Algebra System Of Linear Equations
03/01/20
please help me I need to pass
You have one type of nut that sells for $3.10/lb and another type of nut that sells for $5.70/lb. You would like to have 5.2 lbs of a nut mixture that sells for $4.00/lb. How much of each nut will...
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02/28/20
Systems of Linear Equations Question
Find all the solutions to the following linear system:y/x + 2x/y = 6/xyx2 + y2 = 5
02/28/20
Linear Systems Question
Let t ∈ R and consider the linear system described by the following augment matrix:
A = [ 1 -1 | 0 ]
[ 1 1 | 1 ]
[ 0 1 | t ]
For which values t does this system have:(i) no solutions(ii)...
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Linear Algebra Linear Transformations
02/28/20
Linear Transformation Question
Suppose u = (2, 1, -1)/√6 and let Pu be the linear transformation that projects R3 onto the line through the origin in the direction of the unit vector u. Find all vectors v ∈ R3 with the property...
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Linear Algebra
02/25/20
My question is about matrices.
Hello, i have a question. Suppose A is a 3*2 matrix, B is a p*q matrix and C is a 5*4 matrix. if ABC is defined then p and q is :1) p=2 and q=5 2) p=2 and q=43) p=3 and q=44) p=3 and q=5I...
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Linear Algebra Algebra 2
02/25/20
simultaneous equations
Equation 1: 3x + y - 2z = -7Equation 2: -az = x + y + 6To form the third equation use the digits 2,2,1,9 will be the coefficients of x,y,z, and the constant term in that order, given that the...
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Linear Algebra Algebra 2
02/24/20
Linear problem/question
BIll inherited $25,000 and invested part of it in a money market account, part in bonus bonds and part in a mutual fund. After one year, he received a total of $1,620 in simple interest from the...
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02/24/20
True or False Linear Systems
Determine which of the following statements are true and which are false. (a) The equation 4x − sin(1)y + 2z = 3√5 is linear.(b) The equation xy + 4z = 4 is linear. (c) If a system of linear...
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02/24/20
Systems of Linear Equations Questions
Find all solutions to the following systems of linear equations: (a) x + y = −5 2x − 4y = −4 (b) x + y − z = 1 x + 2y + 2z = 1 2x + y − 5z = 2
02/24/20
Linear Systems Equation Solutions Questions
Determine how many solutions each of the following linear systems have:(a) 6x + 8y = 5 −2x + 9y = −6 (b) 5x + 2y + z = 4 −x + 8y + z = −2 (c) 2x − 3y = −1 3x + y = −4 x − 7y = 2 (d) x + 3y + 3z = 3...
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Linear Algebra
02/24/20
Topic on Linear Algebra .
Which of the following statements is correct ? 1) The solution of 0x+0y = 0 is x= 0 and y= 0 2) (-1;2;4) is a solution of 2x+2y+2z = 10 and 2x-z = 2 please assist.
Need help solving "x*0.096+(1-x)*0.078=0.0888"
i'd like help with solving x please, thanks
Abstract linear algebra
generalize the notions of external and internal direct sums to three or more summands.
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