Mathematics
linear algebra, math homework help

### Question Description

help me solve this assignment.

### Unformatted Attachment Preview

University of Victoria Mathematics 211 M. Laca HW # 2 Summer 2017 Due in class Thursday 25 May 1. Find the distance 1, 1) to the plane through the origin determined by  from  the point  P (4,  1 −5 the vectors ~u =  3  and ~v =  1 . 1 −2 2. For each of the following systems of linear equations: (a) Write the augmented matrix. (b) Obtain a row equivalent matrix in row echelon form. (c) Determine whether the system is consistent or inconsistent. (d) If the system is consistent, write the general solution in standard form.     6 = x +2y +2z −5w −x3 = 6   2x1 +x2 −1 = −x −2y −z +w x1 −2x2 −2x3 = 1 (I) (II) 9 = 4x +8y +5z −8w    −x1 +12x2 +8x3 = 6  7 = 3x +6y +z −5w   1 1 2 1 3. Determine the RREF and the rank of the matrix  2 1 4 3 . 0 3 2 1        4. Show that the set         1 0 1 1 0       ,     1 2 0 0 1       ,       0 1 1 2 −2     ,     1 −3 1 0 1         is linearly dependent and find all     possible ways of writing ~0 as a linear combination of the given vectors (your answer should describe all possible choices of coefficients (α, β, γ, δ) such that ...).     3 3 −5 −6 5. Express ~b =  0  as a linear combination of the columns of A =  0 −1 −1 , or −2 −4 −3 4 show that it is impossible to do so.  6. Let A = 1 0 −1 2 3 4   , B= 4 −1 0 3 −2 3   , 2 C= 5 −1  −3 0 1 −1 −4 2  , 0 0 2   2 D =  −1  . 3 Perform each of the following matrix operations, or indicate that the operation is not defined: a) A + B (b) A + C (c) AB (d) AC (e) DT D (f) DDT  2  0 7. Let fA be the matrix mapping corresponding to A =   5 2 1 2 7 4  0 3  . 9  8 (a) What are the domain and the codomain of fA ? (that is, fA maps what into what?) .  (b) Determine  fA (  −4 2 1   )  3   and fA ( −3 ).  2         (c) Find the images of the standard basis vectors under fA . (d) Write down fA (~x) with formulas. (Your answer should give formulas for the components of fA (~x) in terms of the components of ~x). ...

This question has not been answered.

Create a free account to get help with this and any other question!

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors