Explanation Given Information: The provided table is shown below: Type Air Water Grey matter Tumor Blood Bone Absorption 0 1000 1020 1030 1050 2000 The provided X -ray diagram is shown below: Formula Used: Elementary row operations Type 1: Replacing the row R i by a R i , where a is a nonzero number. Type 2: Replacing the row R i by a R i ± b R j , where a is a nonzero number. Gauss Jordan reduction method: Step 1: First clear the fractions or decimals if any, using operations of type 1. Step 2: Select the first nonzero element of the first row as pivot. Step 3: Use the pivot to clear its column using operations of type 2. Step 4: Select the first nonzero element in the second row a pivot and clear its column. Step 5: Turn all the selected pivot elements into a 1 using operations of type 1. Calculation: Consider the provide table is, Type Air Water Grey matter Tumor Blood Bone Absorption 0 1000 1020 1030 1050 2000 Consider the provided diagram is, To determine the values of each compositions equations can be formed by adding the values along each beams. Add the values along each beam. x + y + u = 4020 And 3 x + 2 u = 8040 Also, 3 y + 2 z = 3000 And 2 z + u = 1020 The augmented matrix for the given system of equations: [ 1 1 0 1 4020 3 0 0 2 8040 0 3 2 0 3000 0 0 2 1 1020 ] Apply Gauss Jordan reduction method to get the solution of the given system of equation. Pivot the first nonzero element of the first row and clear its column. Perform the operations R 2 → R 2 − 3 R 1 . [ 1 1 0 1 4020 3 0 0 2 8040 0 3 2 0 3000 0 0 2 1 1020 ] → [ 1 1 0 1 4020 0 − 3 0 − 1 − 4020 0 3 2 0 3000 0 0 2 1 1020 ] Pivot the first nonzero element of the second row and clear its column. Perform the operations R 1 → 3 R 1 + R 2 , R 3 → R 3 + R 2 . [ 1 1 0 1 4020 0 − 3 0 − 1 − 4020 0 3 2 0 3000 0 0 2 1 1020 ] → [ 3 0 0 2 8040 0 − 3 0 − 1 − 4020 0 0 2 − 1 − 1020 0 0 2 1 1020 ] Next pivot the first nonzero element of the third row and clear its column. Perform the operations R 4 → R 4 − R 3 , [ 3 0 0 2 8040 0 − 3 0 − 1 − 4020 0 0 2 − 1 − 1020 0 0 2 1 1020 ] → [ 3 0 0 2 8040 0 − 3 0 − 1 − 4020 0 0 2 − 1 − 1020 0 0 0 2 2040 ] In the next step, Perform the operation R 4 → 1 2 R 4

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ISBN: 8220103612005

Author: Costenoble

Publisher: CENGAGE L

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Chapter 4.3, Problem 42E

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To calculate: The composition of each of the regions marked by a letters x, y, z and z with the help of provided diagram and table.

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Chapter 4.3, Problem 41E

Chapter 4.3, Problem 43E

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The composition of each of the regions marked by a letters x, y , z and z with the help of provided diagram and table.

Solution Summary: The author explains how to calculate the composition of each of the regions marked by letters x, y, and z with the help of provided diagram and table.

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To calculate: The composition of each of the regions marked by a letters x, y, z and z with the help of provided diagram and table.

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