Task 9: Multiply Two Matrices

Task 10: Transpose of a Matrix

Create a static method named transposeMatrix which accepts a 3 x 3 integer matrix and returns a new 3 x 3 matrix which is the result of switching the rows with the columns in the parameter matrix . Call this method and display the original matrix and the returned matrix.

uIf we switch the rows with the columns in a matrix the resulting new matrix is the Transpose of the original matrix.

Task 11: Symmetric Matrix

Create a static method named isSymmetricMatrix which accepts a 3 x 3 integer matrix and returns true if the matrix is symmetric and false otherwise . Call this method and display the returned boolean value.

A matrix is symmetric if the transpose of the matrix is the same as the original matrix

Task 12: Trace of a Matrix

Create a static method named traceMatrix which accepts a 3 x 3 integer matrix and returns the trace of the matrix. Call this method and display the returned value.

The trace of a matrix is the sum of the values on the main diagonal

Task 13: Determinant of a 3 x 3 Matrix

Create a static method named determinant3x3Matrix which accepts a 3 x 3 integer matrix and returns the determinant of the matrix. Call this method and display the returned value.

The determinant of a 3 x 3 matrix is calculated by:

det(M) = (A x E x I) + (B x F x G) + (C x D x H) (C x E x G) (B x D x I) (A x F x H)

Task 14: Powers of a Matrix

Create a static method named powerNMatrix which accepts a 3 x 3 integer matrix and an integer value and returns a new matrix which is the parameter matrix raised to the power of the parameter integer. Call this method and display the returned matrix.

uM3 = M x M x M

This is what I have so far from the previous tasks:

Task 1 : Display Matrix

public static displaymatrix(int[][] M)

{

for(int i=0;i

{

for(int j=0;j

{

System.out.println(M[i][j]+" ");

}

System.out.println();

} Task 2 : Creat a Matrix

public static int[][] buildMatrix(int v[])

{

int res[3][3];

static int k=0;

for(int i=0;i<3;i++)

{

for(int j=0;j<3;j++)

{

res[i][j]=v[k];

k++;

}

}

return res;

}

Task 3: Create a Matrix

public static int[][] buildRandomMatrix()

{

int[3][3] rmatrix; for (int i=0; i<3; i++)

{

for (int j=0; j<3; j++){

rmatrix[i][j] = (int) (Math.random()*10);

} }

return rmatrix

}

4.Create a Matrix

public static int[][] buildVectorMatrix(int[] a ,int[] b,int[] c)

{

int res[3][3],k=0;

for(int i=0;i<3;i++)

{

for(int j=0;j<3;j++)

{

if(i==0)

res[i][j]=a[k++];

if(i==1)

res[i][j]=b[k++];

if(i==2)

res[i][j]=c[k++];

}

}

Task 5: Compare Two Matrices

public static bool compareMatrices(int[][] M,int[][] N)

{

 int flag = 1; for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) if (M[i][j] != N[i][j]) flag = 0; if (flag == 1) return true; else return false; 

}

Task 6: Add two matrices

public static int[][] addMatrices(int[] M,int[] N)

{

int C[][] = new int[3][3];

for (i = 0; i < 3; i++)

for (j = 0; j < 3; j++)

C[i][j] = M[i][j] + N[i][j];

return C;

}

Task 7: Subtract two matrices

public static int[][] subtractMatrices(int[] M,int[] N)

{

int C[][] = new int[3][3];

for (i = 0; i < 3; i++)

for (j = 0; j < 3; j++)

C[i][j] = M[i][j] - N[i][j];

return C;

}

Task 8: Scalar Multiplication of Matrices

public static scalarProductMatrix(int[][] M,int scalarvalue)

{

for (int i = 0; i < 3; i++)

for (int j = 0; j < 3; j++)

M[i][j] = M[i][j] * scalarvalue;

return M;

}