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Williams - Linear Algebra with Applications 8/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 4 / 19

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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4/19 (21.1%)

  • Instructions

    Here are some textbook questions from Linear Algebra with Applications 8/e by Gareth Williams published by Jones & Bartlett Learning.

    Every problem includes a link to the appropriate section of a complete interactive eBook, (also available through a dynamic table of contents from the student's WebAssign homepage), allowing students to highlight and take notes as they read.

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1. –/6 points WilLinAlg8 2.R.001. My Notes
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–/6
 
Let
A =
30
1−1
, B =
30
63
, C =
1−13
90−2
, and D =
2
8
.


Compute the following (if they exist). (If an answer does not exist, enter DNE into any cell of the matrix.)
(a)    2AB
(b)    AB + C
(c)    BA + AB
(d)    AD − 3D
(e)    AC + BC
(f)    2DA + B
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2. –/2 points WilLinAlg8 2.R.003. My Notes
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Points
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1 2
–/1 –/1
0/50 0/50
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–/2
 
If
A =
1−3
04
, B =
12−3
50−1
, and C =
2−45
710
,
 determine the following elements of
D = 2AB − 3C,
 without computing the complete matrix.
(a)    D12


(b)    D21
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3. –/2 points WilLinAlg8 2.R.007. My Notes
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–/2
 
Find a subspace of solutions for the following homogeneous system of linear equations. Give a basis and the dimension of the subspace.
x1 + x2 + 7x3 + 5x4 = 0
x1 + 5x2 + 3x3 + x4 = 0
2x1 + 7x2 + 9x3 + 5x4 = 0
basis    

dimension    
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4. –/1 points WilLinAlg8 2.R.010. My Notes
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1
–/1
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–/1
 
Use the matrix inverse method to solve the following system of equations.
x1 + 3x2 − 2x3 = −2
2x1 + 5x2 − 3x3 = 0
−3x1 + 2x2 − 4x3 = 5
(x1, x2, x3) = 
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5. –/5 points WilLinAlg8 2.R.012. My Notes
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–/5
 
Verify the associative property of multiplication
A(BC) = (AB)C
 on the given matrices.
A = 
23
56
    B = 
33
22
    C = 
14
42
(a) Find A(BC).
23
56
   ×
=

(b) Find (AB)C.
× 
14
42
 		=

(c) Does
A(BC) = (AB)C?

    
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6. –/2 points WilLinAlg8 2.R.022. My Notes
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–/2
 
Determine whether the following transformations are linear.
(a)    
T(x, y) = (3x, y, y − x)
 of R2 → R3
    

(b)    
T(x, y) = (x + y, 4y + 2)
 of R2 → R2
    
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7. –/1 points WilLinAlg8 2.R.027. My Notes
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1
–/1
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–/1
 
Find the equation of the image of the line
y = −3x + 1
 under a scaling of factor 3 in the x-direction and factor 4 in the y-direction.
y =
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