Let A {a, b, c} and D {1, 2, 3} Let R = (A times B){(a,1)} Wha

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Let A - {a, b, c} and D - {1, 2, 3}. Let R = (A times

B)/{(a,1)} What is the matrix A? Draw the diagram for R in

such a way that no arrows cross. (It is famously to draw

such a diagram for the relation A times D itself.) Consider

and the set 13 How many different relations are there from

A to B! [Caution: a relation from A to D is a subset of A

times B. not an element of A times 13.

Solution

public class Matrix4x4 { private double[] m_; // of 16

/** * Construct a 4x4 identity matrix. */ public

Matrix4x4() { initialize(); setIdentity(); } /** *

Construct a 4x4 matrix with the specified element values.

* * @param m Array of 16 matrix elements, m00, m01,

etc. */ public Matrix4x4 (double[] m) { initialize();

set (m); } /** * Constrauct a 4x4 matrix as a copy

of the specified matrix. * * @param matrix Matrix to

copy. */ public Matrix4x4 (Matrix4x4 matrix) {

initialize(); set (matrix); } /** * Construct a 4x4

matrix with the specified values. * * @param m00

Value of element m[0,0]. * @param m01 Value of

element m[0,1]. * @param m02 Value of element m[0,2].

* @param m03 Value of element m[0,3]. * @param m10

Value of element m[1,0]. * @param m11 Value of

element m[1,1]. * @param m12 Value of element m[1,2].

* @param m13 Value of element m[1,3]. * @param m20

Value of element m[2,0]. * @param m21 Value of

element m[2,1]. * @param m22 Value of element m[2,2].

* @param m23 Value of element m[2,3]. * @param m30

Value of element m[3,0]. * @param m31 Value of

element m[3,1]. * @param m32 Value of element m[3,2].

* @param m33 Value of element m[3,3]. */ public

Matrix4x4 (double m00, double m01, double m02, double

m03, double m10, double m11, double m12,

double m13, double m20, double m21, double

m22, double m23, double m30, double m31,

double m32, double m33) { initialize(); set (m00,

m01, m02, m03, m10, m11, m12, m13, m20,

m21, m22, m23, m30, m31, m32, m33); } /**

* Initialize the matrix. */ private void initialize() { m_

= new double[16]; } /** * Make an identity matrix

out of this 4x4 matrix. */ public void setIdentity() {

for (int i=0; i<4; i++) for (int j=0; j<4; j++) m_[i*4

+ j] = i == j ? 1.0 : 0.0; } /** * Set the value of this

4x4matrix according to the specified * matrix * *

@param matrix Matrix to copy. */ public void set

(Matrix4x4 matrix) { for (int i=0; i<16; i++) m_[i] =

matrix.m_[i]; } /** * Set the values of this 4x4

matrix. * * @param m Array of 16 matrix elements,

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Let A - {a, b, c} and D - {1, 2, 3}. Let R = (A times B)/{(a,1)} What is the matrix A? Draw the diagram for R in such a way that no arrows cross. (It is famously to draw such a diagram for the relation A times D itself.) Consider and the set 13 How many different relations are there from A to B! [Caution: a relation from A to D is a subset of A times B. not an element of A times 13. Solution public class Matrix4x4 { /** private double[] m_; // of 16 * Construct a 4x4 identity ma trix. Matrix4x4() { initialize(); */ public setIdentity(); } /** * Construct a 4x4 matrix with the specified element values. * * @param m Array of 16 matrix elements, m00, m01, etc. */ public Matrix4x4 (double[] m) set (m); } /** */ initialize(); initialize(); * Constrauct a 4x4 matrix as a copy of the specified matrix. copy. { * * @param matrix Matrix to public Matrix4x4 (Matrix4x4 matrix) set (matrix); } matrix with the specified values. Value of element m[0,0]. element m[0,1]. { /** * Construct a 4x4 * * @param m00 * @param m01 Value of * @param m02 Value of element m[0,2]. * @param m03 Value of element m[0,3]. Value of element m[1,0]. * @param m10 * @param m11 Value of element m[1,1]. * @param m12 Value of element m[1,2]. * @param m13 Value of element m[1,3]. Value of element m[2,0]. element m[2,1]. * @param m21 Value of * @param m22 Value of element m[2,2]. * @param m23 Value of element m[2,3]. Value of element m[3,0]. element m[3,1]. * @param m20 ...
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