2x1 +3x2 -x3 =15&nbsp;4x2 +2x3 =16&nbsp; 3x1 +2x3=18&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

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2x1 +3x2 -x3 =15&amp;nbsp;4x2 +2x3 =16&amp;nbsp; 3x1 +2x3=18&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;

karton · Accepted Answer

To solve the system of equations:2x1+3x2−x3=154x2+2x3=163x1+2x3=18We can use the method of Gaussian elimination or matrix operations.First, let&#039;s write the system of equations in matrix form:(23−1042302)(x1x2x3)=(151618)We will perform row operations to transform the coefficient matrix into row-echelon form.Step 1: Subtract 32 times the first row from the third row:(23−10420−9272)(x1x2x3)=(1516−32)Step 2: Multiply the second row by 14:(23−101120−9272)(x1x2x3)=(154−32)Step 3: Add 94 times the second row to the third row:(23−1011200114)(x1x2x3)=(154218)The coefficient matrix is now in row-echelon form.Now, we can solve for the variables using back substitution.From the last equation, we have:114x3=218Multiplying both sides by 411, we get:x3=4288=2144Substituting this value of x3 back into the second equation, we have:x2+12(2144)=4Multiplying both sides by 2, we get:2x2+2144=8Subtracting 2144 from both sides, we obtain:2x2=8−2144Simplifying:2x2=35244−2144=33144Dividing both sides by 2, we have:x2=33188Finally, substituting the values of x2 and x3 into the first equation, we get:2x1+3(33188)−(2144)=15Multiplying both sides by 88 to clear the fractions, we obtain:176x1+331·3−2·21=1320Simplifying:176x1+993−42=1320176x1=1320−993+42176x1=369Dividing both sides by 176, we get:x1=369176Therefore, the solution to the system of equations is:x1=369176, x2=33188, and x3=2144.

2x1 +3x2 -x3 =15 4x2 +2x3 =16  3x1

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