# y y = 4x + 1 y = 3x + 1 in Software Maker QR Code 2d barcode in Software y y = 4x + 1 y = 3x + 1

19 y y = 4x + 1 y = 3x + 1
Paint QR Code JIS X 0510 In None
Using Barcode generator for Software Control to generate, create QR image in Software applications.
QR Recognizer In None
Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications.
y = x + 1 (0,1) x Each axis increment is 1 unit y = 2x + 1
QR Code Drawer In C#
Using Barcode maker for Visual Studio .NET Control to generate, create QR Code image in .NET applications.
QR Code 2d Barcode Encoder In .NET Framework
Using Barcode maker for ASP.NET Control to generate, create QR Code image in ASP.NET applications.
Figure B-10 Illustration for the solution to Prob 10
Printing Quick Response Code In Visual Studio .NET
Using Barcode creator for .NET framework Control to generate, create QR-Code image in .NET applications.
QR Code JIS X 0510 Encoder In Visual Basic .NET
Using Barcode maker for Visual Studio .NET Control to generate, create Denso QR Bar Code image in .NET framework applications.
in Chap 18
Making Barcode In None
Using Barcode creation for Software Control to generate, create barcode image in Software applications.
Print Bar Code In None
Using Barcode encoder for Software Control to generate, create bar code image in Software applications.
Check! Finally the fourth: y = 4x + 1 1=4 0+1 1=0+1 1=1 We can now be confident that the solution to the system is indeed x = 0 and y = 1 10 Figure B-10 shows graphs of all four equations on the Cartesian plane It s visually apparent that if we choose any pair or triplet of these lines, they intersect at the point (0, 1) and nowhere else Therefore, any pair or triplet of the equations, taken as a twoby-two or three-by-two linear system, has the unique solution x = 0 and y = 1
Draw EAN13 In None
Using Barcode drawer for Software Control to generate, create GS1 - 13 image in Software applications.
Make ECC200 In None
Using Barcode creator for Software Control to generate, create DataMatrix image in Software applications.
19
UPC-A Generation In None
Using Barcode generator for Software Control to generate, create UPC-A Supplement 5 image in Software applications.
Code 128 Code Set C Drawer In None
Using Barcode generation for Software Control to generate, create Code 128 Code Set B image in Software applications.
1 Here are the original three equations, stated again for convenience, followed by the step-by-step processes that get the equations into form for conversion to a matrix: x=y z 7 y = 2x + 2z + 2 z = 3x 5y + 4
Painting EAN-8 In None
Using Barcode creator for Software Control to generate, create EAN 8 image in Software applications.
Bar Code Creator In Objective-C
Using Barcode drawer for iPad Control to generate, create barcode image in iPad applications.
656 Worked-Out Solutions to Exercises: s 11 to 19
Painting Bar Code In Java
Using Barcode drawer for Android Control to generate, create bar code image in Android applications.
Draw Data Matrix ECC200 In .NET Framework
Using Barcode printer for Visual Studio .NET Control to generate, create ECC200 image in Visual Studio .NET applications.
We morph the first equation as follows: x=y z 7 x y = z 7 x y + z = 7 Next, the second equation: y = 2x + 2z + 2 2x + y = 2z + 2 2x + y 2z = 2 Finally, the third: z = 3x 5y + 4 3x + z = 5y + 4 3x + 5y + z = 4 Now we have this set of equations representing our three-by-three linear system: x y + z = 7 2x + y 2z = 2 3x + 5y + z = 4 2 Before we write down the matrix, we must be sure we have the correct signs for the coefficients Subtraction of a positive is equivalent to addition of a negative With that in mind, we can pigeonhole the coefficients into the matrix form:
Make GTIN - 13 In Visual Studio .NET
Using Barcode printer for Reporting Service Control to generate, create EAN-13 Supplement 5 image in Reporting Service applications.
Drawing 2D Barcode In Java
Using Barcode maker for Java Control to generate, create Matrix 2D Barcode image in Java applications.
1 2 3 1 1 5 1 2 1 7 2 4
ECC200 Printer In Visual Studio .NET
Using Barcode creation for Reporting Service Control to generate, create DataMatrix image in Reporting Service applications.
Scan EAN-13 Supplement 5 In VB.NET
Using Barcode recognizer for .NET Control to read, scan read, scan image in .NET framework applications.
3 It s easy to convert a matrix into a set of linear equations, but we must pay attention to the signs Here s the matrix:
0 5 1 4 3/2 1 1 8 1 2 1 1
19
Here are the equations, derived directly from the coefficients in the matrix: 0x + 4y + ( z) = 2 5x + ( 3/2)y + 8z = 1 x+y+z=1 Here are the equations with the negative additions converted to subtractions, and the term 0x eliminated from the first equation for simplicity: 4y z = 2 5x (3/2)y + 8z = 1 x+y+z=1 4 Here s the matrix again, for reference:
0 5 1 4 3/2 1 1 8 1 2 1 1
Let s interchange the first and second rows Then we get
5 0 1 3/2 4 1 8 1 1 1 2 1
If we multiply the first row by 2 to get rid of the fractional expression, we have
10 0 1 3 4 1 16 1 1 2 2 1
We can multiply the bottom row by 10, getting
10 0 10 3 4 10 16 1 10 2 2 10
Adding the first row to the third and then replacing the third row with the sum, we obtain
10 0 0 3 4 13 16 1 6 2 2 8
658 Worked-Out Solutions to Exercises: s 11 to 19
Now let s multiply the second row by 13 and the third row by 4 That gives us
10 0 0 3 52 52 16 13 24 2 26 32
Adding the second row to the third and then replacing the third row with the sum, we get
10 0 0 3 52 0 16 13 11 2 26 58
This matrix is in echelon form 5 We want to put the matrix from solution to Prob 4 into diagonal form We can multiply the second row by 11 and the third row by 13 to obtain
10 0 0 3 572 0 16 143 143 2 286 754
Adding the second row to the third and then replacing the second row with the sum, we get
10 0 0 3 572 0 16 0 143 2 1,040 754
Now let s multiply the first row by 572 and the second row by 3 That produces
5,720 0 0 1,716 1,716 0 9,152 0 143 1,144 3,120 754
Adding the first row to the second and then replacing the first row with the sum gives us
5,720 0 0 0 1,716 0 9,152 0 143 1,976 3,120 754
19
We need to turn the 9,152 in the first row into 0 We ll have to work with the third row to make it happen Suppose 9,152 divides cleanly by 143 Let s give it a try A calculator tells us that 9,152 / 143 = 64 Let s multiply the third row by 64 to get the matrix
5,720 0 0 0 1,716 0 9,152 0 9,152 1,976 3,120 48,256
Copyright © OnBarcode.com . All rights reserved.