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Analysis 1: The electrical currents flowing in the antennas, Figure 1(b), during an MR imaging scan are given by: 3i, + 34 - Si -7.5 A- 7i + 2i, -- 17.5 - 10, + 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. 4. Determine i, kzand is by using the Inverse Matrix Method.

Analysis 1: The electrical currents flowing in the antennas, Figure 1(b), during an MR imaging scan are given by: 3i, + 34 - Si -7.5 A- 7i + 2i, -- 17.5 - 10, + 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. 4. Determine i, kzand is by using the Inverse Matrix Method.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text: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.
Transcribed Image Text: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.
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