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Williams - Linear Algebra w Applications (alt) 8/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 4 / 23

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

Last Saved : n/a Saving...  ()

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4/23 (17.4%)

  • Instructions

    Here are some textbook questions from Linear Algebra with Applications (alternate edition) 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 WilLinAlgAlt8 2.R.001. My Notes
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–/6
 
Let
A =
60
8−1
, B =
40
53
, C =
5−13
90−2
, and D =
9
5
.


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 WilLinAlgAlt8 2.R.003. My Notes
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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. –/3 points WilLinAlgAlt8 2.R.007. My Notes
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–/3
 
Determine the inverse of each of the following matrices, if it exists, using the method of Gauss-Jordan elimination. (If an answer does not exist, enter DNE.)
(a)    
43
1−4
(b)    
3−1−1
−211
−241218
(c)    
3−2−4
−112
−337
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4. –/1 points WilLinAlgAlt8 2.R.008. 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 = −6
2x1 + 5x2 − 3x3 = −7
−3x1 + 2x2 − 4x3 = 6
(x1, x2, x3) = 
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5. –/5 points WilLinAlgAlt8 2.R.010. 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
34
    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. –/3 points WilLinAlgAlt8 2.R.014. My Notes
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–/3
 
A matrix is said to be normal if
AAt = AtA.
 Show that the given symmetrical matrix is normal.
A = 
624
242
426
(a) Find AAt.
(b) Find AtA.
(c) Does
AAt = AtA
 for all symmetric matrices?
    
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7. –/3 points WilLinAlgAlt8 2.R.022. My Notes
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–/3
 
The following stochastic matrix P gives the probabilities for a certain region of college and noncollege educated households having at least one college educated child. By a college educated household we understand that at least one parent is college educated, while by noncollege educated we mean that neither parent is college educated.
household
coll ed   noncoll ed
P = 
 		0.9 0.25
college educated  child
0.1 0.75 noncollege educated
If there are currently 500,000 college educated households and 900,000 noncollege educated households what is the predicted distribution for two generations hence?
college educated
noncolledge educated


What is the probability that a couple that has no college education will have at least one grandchild with a college education?
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