1,975 Answered Questions for the topic linear algebra

08/28/16

For which values parameter x,y system equations with two unknowns have unique solution,inconsistent or infinitely many solutions?
Determine for which values parameter x,y system equations with two unknowns have unique solution,inconsistent or infinitely many solutions.  ax+by=c^2  a+x/b=b+y/a , a≠o,b≠o   and another... more
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Linear Algebra

08/07/16

Linear Transformation
L : V → W is a linear transformation, and v1≠ 0, L(v1) = 0, L(v2) ≠ 0, show that v1, v2 are linearly independent.
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Linear Algebra

08/07/16

Vector Space and Basis
Explain why a vector space V can’t have both {v1, v2} (v1 and v2 are distinct)and {w1, w2, w3} (w1, w2, w3 are distinct) as its basis. (You’re not allowed to cite anytheorem, but only the... more
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Linear Algebra Functions

07/17/16

Linear Algebra
In one part of the? world, the sea lion population decreased approximately linearly from about 60 thousand in 1990 to about 24 thousand in 2003. Find the average rate of change of the sea lion... more
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Linear Algebra Math Linear Equations Vector

07/10/16

Let V be the vector set in R2 with the following: Addition: [x1x2]?[y1y2]=[0x2+y2] Scalar Multip.: a?[x1x2]=[0ax2] Which of 8 Vector Space Axioms are met?
I cannot for the life of me figure out which of these I am missing and/or over-including in my response to this question.
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Linear Algebra Transition Matrix

07/04/16

Change of Basis
Define u_1=?(1,1,0)?^T,u_2=?(0,1,1)?^T,u_3=?(1,0,1)?^T and v_1=?(1,1,2)?^T,v_2=?(2,1,1)?^T,v_3=?(1,2,1)?^T, then obtain the transition matrix from (v1,v2,v3) to (u1,u2,u3) and also from (u1,u2,u3 )... more
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Linear Algebra

05/29/16

Find A^100
Consider the Matrix A=                                                                                                                                                [ 1 -2 8 ]  [ 0 -1 0 ] [ 0 0... more
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Linear Algebra

05/29/16

consider the matrix A
Consider the matrix A = [  1  3  0]                                     [3    1  0]                                    [0   0  -2]     (a) find the eigenvalues for A (b) Find a matrix P such... more
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Linear Algebra

05/26/16

Prove the following results for the eigenvalues of a n * n matrix A.
Prove the following results for the eigenvalues of a n * n matrix A. (a) 0 is an eigenvalue for A if and only if A is non invertible.(b) A and A^T have the same eigenvalues.
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Linear Algebra

05/12/16

Suppose linear transformation L : R2 ?R3 is de?ned by:
Suppose linear transformation L : R2 →R3 is de?ned by:   L [ x ]    = [ 3x-y]    [ y]        [ x+y]                 [    -x]   find the Matrix of L:   1) with respect to the standard bases... more
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Linear Algebra

05/12/16

Find the kernel of L. Is the transformation L injective AND Find the image of L. Is the transformation L surjective
Let A= [3   1 ]           [1   -2]    and L be the transformation defined by :                   or A can be written as A=(3,1,2),(1,-2,2)           [2   2 ]   L (X) = AX ,L : R2... more
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Linear Algebra

05/11/16

Fit a regression line to the points (0,0), (1,2), (2,7)
Fit a regression line to the points (0,0), (1,2), (2,7)
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Linear Algebra

05/11/16

Use the Gram-Schmidt process to transform the basis {u1,u2,u3} into an orthonormal basis
Let R3 have the Euclidean inner product and   u1= [2]       u2= [1 ]    u3= [4 ]        [-2]            [-1]           [-3]                    or it can be written as u1(2,-2,1),  u2(1,-1,5) and... more
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Linear Algebra

05/11/16

Show that {v1,v2,v3} is an orthonormal basis in R3 with the Euclidean inner product
Consider Vector:   v1= 1/sqrt(18)  [  4 ]  ,   v2= 1/3  [ 1 ] ,   v3= 1/sqrt(2)  [0],   w= [2]                        [ -1 ]                    [ 2 ]                          [1]         [1]    ... more
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Linear Algebra

04/27/16

how many yearbooks should your school order?
Your student Gov. surveryed three homeroom classes, and 55 of 90 students said that they would definitely buy a yearbook. If your school has 2000 students, approximately how many books should be... more
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Linear Algebra

04/06/16

Y=6 when x= 4
Write the inverse variation equation, given that x and y vary inversely.  
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Linear Algebra

04/06/16

Help with least squares
Find the least squares solution of the system AX=B.    Where A = a 4X3 matrix {[1 -1 1] [1 1 1] [0 1 1] [1 0 1] } and b = a 4X1 matrix {[2 1 0 2]}.   I have calculated A⊥A which ={[3 0 3] [0 3... more
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Linear Algebra

04/06/16

Find least Square regression
Find the least squares regression line for the data points (1,1),(2,3),(4,5)
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Linear Algebra

04/05/16

Lodine-131 has half-life of 8 days. How much iodine will you have after 24 days if you start with 60 milligrams?
Thank you for help me
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Linear Algebra

04/04/16

Consider two bases for R2
 Consider two bases for R2   B= { [ 1 ] , [-1] }  and B' ={ [ 2 ], [ 4 ] }           3       -1                       2      -1   1) Find the transition matrix from B to B' . 2) Vector u has... more
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Linear Algebra Vector Calculus

04/01/16

Linear Algebra (Vector Space)
Determine whether s is a basis for the indicated vector space S= {(1,2),(1,-1)} for R2 
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Linear Algebra

03/18/16

Prove that if A^T A = In, then detA = ±1.
Prove that if A^T A = In, then detA = ±1.
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Linear Algebra

03/18/16

Find det(cA) in terms of c and detA.
Find det(cA) in terms of c and detA.
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Linear Algebra

03/18/16

Show that det In = 1
Show that det In = 1
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Linear Algebra

03/18/16

consider the following linear system
consider the following linear system x+z=1 y+z=2 2y+cz=c for which values of c does the system have (i) a unique solution, (ii) many solution, (iii) no solution
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