LMS Integrated for MindTap Engineering, 2 terms (12 months) Printed Access Card for Moavni's Engineering Fundamentals: An Introduction to Engineering, 5th
LMS Integrated for MindTap Engineering, 2 terms (12 months) Printed Access Card for Moavni's Engineering Fundamentals: An Introduction to Engineering, 5th
5th Edition
ISBN: 9781305110366
Author: Saeed Moaveni
Publisher: Cengage Learning
bartleby

Concept explainers

Construction Documents
Construction documents are the branch of architectural design and a vital field of the architectural process. We must not mistake the construction documents as a schematic design, wherein it involves sketching, model making, and so on. They provide guida…
Question
Book Icon
Chapter 18, Problem 17P

(a)

To determine

Find the addition of matrix [A]and [B].

(a)

Expert Solution
Check Mark

Answer to Problem 17P

The addition of matrix [A] and [B] is [540123−450−4].

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

[C]=[1−24]

Calculation:

Add two matrixes [A] and [B],

[A]+[B]=[42170−71−53]+[12−153345−7] (1)

Reduce the equation (1) as follows,

[A]+[B]=[4+12+21−17+50+3−7+31+4−5+53−7]=[540123−450−4]

Therefore, the addition of matrix [A] and [B] is [540123−450−4].

Conclusion:

Thus, the addition of matrix [A] and [B] is [540123−450−4].

(b)

To determine

Find the subtraction of matrix [A] and [B].

(b)

Expert Solution
Check Mark

Answer to Problem 17P

The subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Explanation of Solution

Given data:

[A]=[42170−71−53],

[B]=[12−153345−7] and

Calculation:

Subtract two matrixes A and B

[A]−[B]=[42170−71−53]−[12−153345−7] (2)

Reduce the equation (2) as follows,

[A]−[B]=[4−12−21−(−1)7−50−3−7−31−4−5−53−(−7)]=[3022−3−10−3−1010]

Therefore, the subtraction of matrix [A] and [B] is [3022−3−10−3−1010].

Conclusion:

Thus, the subtraction of matrix A and B is [3022−3−10−3−1010].

(c)

To determine

Find the value of 3[A].

(c)

Expert Solution
Check Mark

Answer to Problem 17P

The value of 3[A] is [1263210−213−159].

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Three times of matrix [A] is,

3[A]=3[42170−71−53] . (3)

Reduce equation (3) as follows,

3[A]=3[42170−71−53]3[A]=[3×43×23×13×73×03×(−7)3×13×(−5)3×3]

3[A]=[1263210−213−159]

Therefore, the value of  3[A] is [1263210−213−159].

Conclusion:

Thus, the value of  3[A] is [1263210−213−159].

(d)

To determine

Find the multiplication of matrix [A] and [B].

(d)

Expert Solution
Check Mark

Answer to Problem 17P

The multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Explanation of Solution

Given data:

A=[42170−71−53]

B=[12−153345−7]

C=[1−24]

Calculation:

Multiply the matrix [A] and [B],

[A][B]=[42170−71−53][12−153345−7] (4)

Reduce equation (4) as follows,

[A][B]=[42170−71−53][12−153345−7]=[4(1)+2(5)+1(4)4(2)+2(3)+1(5)4(−1)+2(3)+1(−7)7(1)+0(5)+(−7)(4)7(2)+0(3)+(−7)(5)7(−1)+0(3)+(−7)(−7)1(1)+(−5)(5)+3(4)1(2)+(−5)(3)+3(5)1(−1)+(−5)(3)+3(−7)]=[1819−5−21−2142−122−37]

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

Conclusion:

Therefore, the multiplication of matrix [A] and [B] is [1819−5−21−2142−122−37].

(e)

To determine

Find the multiplication of matrix [A] and [C].

(e)

Expert Solution
Check Mark

Answer to Problem 17P

The multiplication of matrix [A] and [C] is [4−2123].

Explanation of Solution

Given data:

[A]=[42170−71−53]

[C]=[1−24]

Calculation:

Multiply the matrix [A] and [C],

[A][C]=[42170−71−53][1−24] (5)

Reduce equation (5) as follows,

[A][C]=[42170−71−53][1−24]=[4(1)+2(−2)+1(4)7(1)+0(−2)+(−7)(4)1(1)+(−5)(−2)+3(4)]=[4−2123]

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

Conclusion:

Therefore, the multiplication of matrix [A] and [C] is [4−2123].

(f)

To determine

Find the square of matrix [A].

(f)

Expert Solution
Check Mark

Answer to Problem 17P

The square of matrix [A] is [1819−5−21−2142−122−37].

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

Square of the matrix [A],

[A]2=[A][A][A][A]=[42170−71−53][42170−71−53] (6)

Reduce equation (6) as follows,

[A]2=[42170−71−53][42170−71−53]=[4(4)+2(7)+1(1)4(2)+2(0)+1(−5)4(1)+2(−7)+1(3)7(4)+0(7)+(−7)(1)7(2)+0(0)+(−7)(−5)7(1)+0(−7)+(−7)(3)1(4)+(−5)(7)+3(1)1(2)+(−5)(0)+3(−5)1(1)+(−5)(−7)+3(3)]=[313−72149−14−28−1345]

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

Conclusion:

Therefore, the square of matrix [A] is [313−72149−14−28−1345].

(g)

To determine

Prove the operation  [I][A]=[A][I]=A.

(g)

Expert Solution
Check Mark

Explanation of Solution

Given data:

A=[42170−71−53]

Calculation:

[I] is the unit identity matrix [100010001].

Therefore,

[I][A]=[100010001][42170−71−53] (7)

Reduce equation (7) as follows,

[I][A]=[100010001][42170−71−53]=[1(4)+0(7)+0(1)1(2)+0(0)+0(−5)1(1)+0(−7)+0(3)0(4)+1(7)+0(1)0(2)+1(0)+0(−5)0(1)+1(−7)+0(3)0(4)+0(7)+1(1)0(2)+0(0)+1(−5)0(1)+0(−7)+1(3)]=[42170−71−53] (8)

Now,

[A][I]=[42170−71−53][100010001] (9)

Reduce equation (9) as follows,

[A][I]=[42170−71−53][100010001]=[4(1)+2(0)+1(0)4(0)+2(1)+1(0)4(0)+2(0)+1(1)7(1)+0(0)+(−7)(0)7(0)+0(1)+(−7)(0)7(0)+0(0)+(−7)(1)1(1)+(−5)(0)+3(0)1(0)+(−5)(1)+3(0)1(0)+(−5)(0)+3(1)]

[A][I]=[42170−71−53] (10)

Comparing equation (9) and (10),

[I][A]=[A][I]=A

Hence proved

Conclusion:

Thus, the operation [I][A]=[A][I]=A is proved.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Previous
Chapter 18, Problem 16P
Next
Chapter 18, Problem 18P
Students have asked these similar questions
What are some relative code requirements specific to a roof system components?
The ____________ costs can often be the determining factor in a successful project. Group of answer choices Overhead Material Labor Profit
Who is responsible for conducting special inspections and ensuring the work completed complies with design documents and referenced standards, why are specical inspections required?

Chapter 18 Solutions

LMS Integrated for MindTap Engineering, 2 terms (12 months) Printed Access Card for Moavni's Engineering Fundamentals: An Introduction to Engineering, 5th

Ch. 18.2 - Prob. 1BYGCh. 18.2 - Prob. 2BYGCh. 18.2 - Prob. 3BYGCh. 18.2 - Prob. 4BYGCh. 18.2 - Prob. BYGVCh. 18.3 - Prob. 1BYGCh. 18.3 - Prob. 2BYGCh. 18.3 - Prob. 3BYGCh. 18.3 - Prob. BYGVCh. 18.4 - Prob. 1BYG
Ch. 18.4 - Prob. 2BYGCh. 18.4 - Prob. 3BYGCh. 18.4 - Prob. 4BYGCh. 18.4 - Prob. BYGVCh. 18.5 - Prob. 1BYGCh. 18.5 - Prob. 2BYGCh. 18.5 - Prob. 3BYGCh. 18.5 - Prob. 4BYGCh. 18.5 - Prob. BYGVCh. 18.6 - Prob. 1BYGCh. 18.6 - Prob. 2BYGCh. 18.6 - Prob. 3BYGCh. 18.6 - Prob. 4BYGCh. 18.6 - Prob. BYGVCh. 18.7 - Prob. 1BYGCh. 18.7 - Prob. 2BYGCh. 18.7 - Prob. BYGVCh. 18 - Prob. 1PCh. 18 - Prob. 2PCh. 18 - Prob. 3PCh. 18 - In Chapter 12, we explained that the electric...Ch. 18 - The deflection of a cantilevered beam supporting...Ch. 18 - Prob. 6PCh. 18 - Prob. 7PCh. 18 - Prob. 8PCh. 18 - Prob. 9PCh. 18 - Prob. 10PCh. 18 - Prob. 11PCh. 18 - Prob. 12PCh. 18 - Prob. 13PCh. 18 - Prob. 14PCh. 18 - A jet plane taking off creates a noise with a...Ch. 18 - Prob. 16PCh. 18 - Prob. 17PCh. 18 - Prob. 18PCh. 18 - Prob. 19PCh. 18 - Prob. 20PCh. 18 - Prob. 21PCh. 18 - Prob. 22PCh. 18 - Prob. 23PCh. 18 - Prob. 24PCh. 18 - Prob. 25PCh. 18 - Prob. 26PCh. 18 - Prob. 27PCh. 18 - Prob. 28PCh. 18 - Prob. 29PCh. 18 - Prob. 30PCh. 18 - Prob. 31PCh. 18 - Prob. 32PCh. 18 - Prob. 33PCh. 18 - Prob. 34PCh. 18 - Prob. 35PCh. 18 - Prob. 36PCh. 18 - Prob. 37PCh. 18 - Prob. 38PCh. 18 - Prob. 39PCh. 18 - Prob. 40PCh. 18 - Prob. 41PCh. 18 - Prob. 42PCh. 18 - Prob. 43PCh. 18 - Prob. 44PCh. 18 - Prob. 45P
Knowledge Booster
Background pattern image
Civil Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Engineering Fundamentals: An Introduction to Engi...
Civil Engineering
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Cengage Learning
Text book image
Fundamentals Of Construction Estimating
Civil Engineering
ISBN:9781337399395
Author:Pratt, David J.
Publisher:Cengage,
SEE MORE TEXTBOOKS