RF Pule!!!Antenna Antenna 2 Antenna 3(c)Figare 1: (a) MR mackine, (b) tkre loop antennas, and (c) brain MR imageThe analysis are as follows:Analysis 1: The electrical currents flowing in the antennas, Figure 1(b), during an MR imaging scan aregiven by:3i, + 3i, - Si; - 7.5i- 7i, + 2i, -- 17.5- 10i, + 4i; + Sis - 161. Write the above system of equations in the form Ax-b, where A is a 3 by 3 matrix and x andbare 3 by 1 vectors.2. Find the determinant of A.3. Determine i, izand is by using Gaussian elimination.4. Determine i, izand is by using the Inverse Matrix Method. You are working as an Engineering Technician at GEMR, which specializes in designing and developingmedical equipment such as Magnetic Resonance Imaging (MRI) systems, X-ray systems, and RadioFrequency (RF) antennas coils. You will be working with the MRI and RF coils team to design a threeantenna RF coil, as shown in Figure 1(b), to be used in conjunction with an MR machine. The RF coil willbe placed on the patient head during the MR scan, see Figure 1(a). The RF coil will be exposed to an RFpulse that is in conjunction with the magnetic field of the MR scanner, Figure 1(a), receives signals fromthe brain as current flowing in the antennas. These currents are then converted into an image of thebrain as seen in Figure 1(c). Your responsibility is to carry out mathematical analysis of the RF coil topredict the performance of the antennas before they can be tested on human beings.

Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

analysis are as lollows: Analysis 1: The electrical currents flowing in the antennas, Figure I(b), during an MR imaging scan are given by: 3i, + 34, - Si, - 7.5 A- 7i + 2i, -- 17.5 - 101, + 4i; + Si - 16 1. Write the above system of equations in the form Ax-b, where A is a 3 by 3 matrix and x and bare 3 by I vectors. 2. Find the determinant of A. 3. Determine i, izand i, by using Gaussian elimination.

analysis are as lollows: Analysis 1: The electrical currents flowing in the antennas, Figure I(b), during an MR imaging scan are given by: 3i, + 34, - Si, - 7.5 A- 7i + 2i, -- 17.5 - 101, + 4i; + Si - 16 1. Write the above system of equations in the form Ax-b, where A is a 3 by 3 matrix and x and bare 3 by I vectors. 2. Find the determinant of A. 3. Determine i, izand i, by using Gaussian elimination.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Use Invere matrix method to solve the following equations: -ut-1 2r - 2y + 2: = 2 -3r +3y +32 =-3

A: Explanation of the solution is given below...

Q: Let A = -2 1 0 3 and B = 2 -3 1 −2. Find a matrix X satisfying the matrix…

A: The given matrices, A=-2103 and B=2-31-2 We have to find the matrix X, that satisfies 2A+X=3B

Q: If A = Find the matrix 22A - 5(A + 2B) + 27B and B = B) 17. 151 -341 51 341

A: From the given problem: A=3-52-4 ; B=-3516 22A-5A+2B+27B...1 So, 22A=223-52-4=66-11044-88…

Q: /0 5 5 8 For the matrix A = 4 5 2 19 4 4/ A. -7 C. - 12 cofactor C₂1? B. 12 D. 7

Q: Q5) ẩ.ẩ jolve the eẩqẩuatẩionj; 2x²y dy/ldx + 2xy' +1= 0

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: The rank of the matrix a = b = c is: 1 a b a² 6² 1 1 C where

A: Given : matrix =[111abca2b2c2]Also given : a=b≠c

Q: Solve the following system by using the inverse of a matrix (X = A¯¹B): 3x + y = 17 -4x+2y=-6

A: Consider the given system of equations.We need to find the solution of the given system using…

Q: 3) Find the inverse of the Matrix: A || -3 6 (39) 4

Q: Solve the following using the inverse matrix method: 2x - y + 3z = 9 x+y+z = 6 x-y+z=2

Q: 2X + 3Y – 2Z = 5 5Y + 3Z = -2 4X – 3Y + Z = 1

A: Matrix form is 2 3 -2 5 0 5 3 -2 4 -3 1 1

Q: d. y= x² + y x + cos y

Q: (-81,24,16)

A: Determinant of matrix is=-5258

Q: Given the matrix R = (3¹), i. show that R is non-singular. find R¹, the inverse of R. ii. iii. show…

Q: Consider the following matrices: -7 M = -1 (4-2) and (NM) - (34) 2 7 T = 1 a) Find matrix N. b)…

A: Step 1: Step 2: Step 3: Step 4:

Q: Using the information in the table below, find the occupancy rate for the years 2021 to 2024 using…

A: Given α=0.3. Let At represent the actual values of the occupancy rate and Ft represent the forecast…

Q: Q2) Solve the following linear system of equations using inverse matrix 3x + y = -1: 2y- 4z = 0 :x+…

A: The system of given linear equations is as follows 3x+y=-12y-4z=0x+2z=1 Rewrite as…

Q: h) Suppose we have the system of 4x – 3y = 5 and 5x + 3y = 4. You found the inverse of matrix A…

Q: QI: Solve the set of equations using matrix: x+ 2y +3z = 1 y + 4z = 0 5x + 6y = 1

Q: Q.2) Use Inverse matrix method to solve the following equations: *- y +z = 1 2r – 2y + 2: = 2 -3r +…

Q: Write the following system of equations as matrix equations Ax=b and solve the computing A-¹b.…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Solve A x A T matrix: A = -2 1 -1 3 -3 2

Q: Consider the simultaneous equations: 4y1 + 7y2 = 25 2y1 + 3y2 = 28 a. Write these equations in…

A: Given, The given simultanous equation is: 4y1 + 7y2 = 252y1 + 3y2 = 28 To find, a. Write…

Q: Consider the system [3x + 5y = 2r - 3y = -13. 9 a. Express the system in the form AX = B, where A,…

A: Inverse of a matrix: The inverse of an n×n matrix A is an n×n matrix B having the property…

Q: Given the matrix: A= [1 -2 1 3]. Perform the operation

Q: a) Consider the matrices A and B: 4 -3 A =-2 7 1 8 6. -5 B = -3 -2 Which element is in row 2, column…

Q: Q1: Solve the set of equations using matrix: x+ 2y +3z 1 y + 4z = 0 5x + 6y = 1

Q: Given 2. A and B = ( 4 Find the matrix represented by: (iii) 3(A – 4B) (iv) B+ 3AT

A: The given matrices are A=254-2 and B=-1724. (iii) Evaluate 3(A-4B) as follows.…

Q: Find the equation (in standard form) of a circle containing points by using the matrices method:…

Q: Use Inverse Matrix to solve the following equations: x – 3y + 2z = 4 -2x – y + z = 5 | x – 2y – 3z =…

Q: Find the matrix representations for R² and R-1.

A: First we define relation matrix for R:

Q: (a) Consider the system of equations 11х3 — Зх1 yi %3D - 7x1 – 6x2 – 5x3 y2 х> + 2х3 — 2х = y3…

Q: Find values for the the entries in the second matrix to satisfy this equation: 30 -25 -13 14 5 5 0 0…

A: Given query is to find the the entries of the matrix.

Q: Q2) Solve the following linear system equations by matrix: 3x + 4y = 2,8y +z 1 and 6x - 5z 7.

A: 2 Given system of linear equations are 3x+4y=28y+z=16x−5z=7.....1 Now, write the system of equations…

Question

100%

RF Pule
!!!
Antenna Antenna 2 Antenna 3
(c)
Figare 1: (a) MR mackine, (b) tkre loop antennas, and (c) brain MR image
The analysis are as follows:
Analysis 1: The electrical currents flowing in the antennas, Figure 1(b), during an MR imaging scan are
given by:
3i, + 3i, - Si; - 7.5
i- 7i, + 2i, -- 17.5
- 10i, + 4i; + Sis - 16
1. Write the above system of equations in the form Ax-b, where A is a 3 by 3 matrix and x and
bare 3 by 1 vectors.
2. Find the determinant of A.
3. Determine i, izand is by using Gaussian elimination.
4. Determine i, izand is by using the Inverse Matrix Method.

You are working as an Engineering Technician at GEMR, which specializes in designing and developing
medical equipment such as Magnetic Resonance Imaging (MRI) systems, X-ray systems, and Radio
Frequency (RF) antennas coils. You will be working with the MRI and RF coils team to design a three
antenna RF coil, as shown in Figure 1(b), to be used in conjunction with an MR machine. The RF coil will
be placed on the patient head during the MR scan, see Figure 1(a). The RF coil will be exposed to an RF
pulse that is in conjunction with the magnetic field of the MR scanner, Figure 1(a), receives signals from
the brain as current flowing in the antennas. These currents are then converted into an image of the
brain as seen in Figure 1(c). Your responsibility is to carry out mathematical analysis of the RF coil to
predict the performance of the antennas before they can be tested on human beings.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Markov Processes and Markov chain$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Pre calc.5
Q3:-a) Find the values of (x, y) for the following matrix equation: 3 [х — 2у 0ј 6. -2 -2 x+ y]
1. Write the following linear system in matrix form. 2x, + 3x₂ -[33] Exercises 1.1 Matrices B = 032 2 -3 7 2 4-5 and E= |--H -4 3. Write the linear system whose augmented matrix is a. 213 4 b. 3-1 2 0 1-4 3 8 2 5 3 7 6 -4 10 14 C 2 3 -1 -2 1 LL 324 1 0 3 0 0 0 0 5 -4 0 2 4 0 03 20 Eel +2. 1, 2 +1 ml me luc
Help me answer the problem using matrices operations with step-by-step complete solutions and box the final answer. Show all solutions by writing them on clean paper. Thank you
Show the following simultaneous equations in matrix form: 4x – 4y – 6 = 0 16y = 14x + 4
b) Consider the matrices C and D: C = D -8 2 at 8.49.35 AM Calculate matrix 2C + 3D. at 8.16.50 AM
9) Solve the set of equations by finding the inverse of the coefficient matrix: x - 2y = 5 3x + y = 15 formation of vectors in