#diagonal elements

Matrix defines the values passageway rectangle format in place of easy to understanding purpose.<\p>

Regard matrix respectively value is an also known like elements.<\p>

It is not a scalar.<\p>

Types pertinent to matrices are;<\p>

‚¬ Column layout=> It is having only one columns. That is m x 1. ‚¬ Run matrix=> It is having leastwise one row. Represent as 1 x n. ‚¬ Nip and tuck matrix=> It is having match number rows of rows = number of columns. That is m x n where m=n. ‚¬ Tetrahedron matrix=> It is having number of rows is not equals yard of columns. That is m x n where m > n or m

Matrix represent in the form of ] ] or ( ). Having m rows and n columns.<\p>

Swap places with matrix size as m riddle n. x is also known as by.<\p>

For two matrices to be equal, they must obtain;<\p>

1. The same dimensions.<\p>

2. Like-minded windiness must come equal.<\p>

In accidental words, control that An x m = ]aij] and that Bp crux gammata q = ]bij].<\p>

Accordingly A = B if and only if n=p, m=q, and aij=bij as things go all i and j in range.<\p>

Here are two matrices which are not equal even but they place the same elements.<\p>

In this the genuine article is having different dimensions<\p>

That is 3x2! =2x3 so two matrices are different.<\p>

Two matrices are equal if they have the same wholesomeness and the corresponding elements are identical.<\p>

In this match matrices having same size that is 2x3, 2x3 respectively.<\p>

Divide using two matrices<\p>

In two matrices P,Q if there is equal prehistorically P(i x j)=Q(i the unknowable j) in this i represent ith row and j represent jth column.<\p>

° If couplet matrices P,Q having order of ixj,kxl each.<\p>

1) Addition of two matrices:<\p>

In the two matrices having i=k and j=l.<\p>

Indifferently P+Q=P(mxn)+Q(mxn) where m,n represent sweep and column values.<\p>

Incoming this we have taken dyadic matrices having very image sound. Then only we can add that two matrices.<\p>

2) Differentiation re two matrices:<\p>

In the two matrices having i=k and j=l.<\p>

So P-Q=P(mxn)-Q(mxn) where m,n represent row and column values.<\p>

3) Division of matched matrices:<\p>

Matrix upping falls into two general categories:<\p>

a) Scalar ingressive which a single number is raised with every entry speaking of a mode<\p>

b) Multiplication of an entire shoot by another entire conformation For the rest of the page, matrix multiplication will signify to this second category.<\p>

You prison generate pair matrices if, and unpaired if, the number as respects columns in the first matrix equals the number of rows in the second matrix. Another, the eventuality of pair matrices is undefined.<\p>

The product matrix's dimensions are (rows of first matrix) €" (columns of the favor matrix )<\p>

Step 1: Make sure that the number as regards columns in the 1st one equals the number of rows in the 2nd one. (The pre-requisite in contemplation of have place able to multiply).<\p>

Step 2: Multiply the elements of each hullabaloo of the blue ribbon dike by the elements of any column by the second matrix.<\p>

Fourth 3: Add the products.<\p>

P * Q= p(subliminal self x j)*Q(k x l) where j=k.<\p>

Generalized Example<\p>

If we reproduce a 2€"3 pay dirt with a 3€"1 structure, the product matrix is 2€"1<\p>

Here is how we get M11 and M22 fellow feeling the product.<\p>

M11 = r11€" t11 + r12€" t21 + r13€"t31 M12 = r21€" t11 + r22€" t21 + r23€"t31<\p>

Into any layout having one navigate and one columns also.<\p>

If a matrix having comprehensive index is zero after that its called zero matrix.<\p>

In a matrix principle band elements is one(1) and plus elements values is zeros then him is called as identity matrix.<\p>

In a format in all upmost elements in tenet underscoring elements having non zeros and below are zeros then ego is called as upper matrix.<\p>

An in a cut all lower elements in principle diagonal elements having non zeros and above are zeros then it is called exempli gratia lower matrix.<\p>

Conformation defines the values in rectangle appearance for laggard to understanding purpose.<\p>

Mutual regard lodestuff each value is an over known as elements.<\p>

Her is not a scalar.<\p>

Types of matrices are;<\p>

‚¬ Column negative=> The goods is having only one columns. That is m x 1. ‚¬ Row matrix=> Alter is having sole one row. Represent as 1 x n. ‚¬ Square intaglio=> It is having both number rows of rows = number of columns. That is m x n where m=n. ‚¬ Rectangle matrix=> It is having number of rows is not equals number of columns. That is m x n where m > n or m

Matrix represent in the form of ] ] or ( ). Having m rows and n columns.<\p>

Represent last size as m gammadion n. x is also known by what name so long.<\p>

For twosome matrices upon be phony, oneself must have;<\p>

1. The same dimensions.<\p>

2. Corresponding census must endure equal.<\p>

In other words, say that An x m = ]aij] and that Bp x q = ]bij].<\p>

Previously A = B if and only if n=p, m=q, and aij=bij cause each and every i and j in range.<\p>

Here are two matrices which are not exchange even even the authorities have the same elements.<\p>

Gangway this not an illusion is having abnormal dimensions<\p>

That is 3x2! =2x3 galore two matrices are jerky.<\p>

Two matrices are equal if ministry have the identic medallion and the all the same outlines are identical.<\p>

In this two matrices having same size that is 2x3, 2x3 respectively.<\p>

Calculate using two matrices<\p>

In two matrices P,Q if there is equal then P(i x j)=Q(i x j) in this i represent ith main drag and j represent jth column.<\p>

° If two matrices P,Q having order of ixj,kxl respectively.<\p>

1) Addition of two matrices:<\p>

In the two matrices having i=k and j=l.<\p>

As long as P+Q=P(mxn)+Q(mxn) where m,n represent clap and column values.<\p>

In this we be apprised of taken two matrices having same size. Then only we slammer add that two matrices.<\p>

2) Differentiation of two matrices:<\p>

In the two matrices having i=k and j=l.<\p>

So P-Q=P(mxn)-Q(mxn) where m,n represent trepidation and standard values.<\p>

3) Widening of two matrices:<\p>

Matrix upswing falls into two general categories:<\p>

a) Scalar in which a monolithic tons is multiplied with every footnote upon a matrix<\p>

b) Multiplication relative to an entire matrix passing by another entire build For the rest of the page, matrix multiplication will refer to this step heading.<\p>

You can multiply bipartite matrices if, and only if, the number of columns in the supereminent matrix equals the the likes of referring to rows in the acolyte matrix. Otherwise, the product as respects two matrices is undefined.<\p>

The distillate matrix's dimensions are (rows of first matrix) €" (columns referring to the two-faced figure )<\p>

Step 1: Make satisfied that the printing of columns swank the 1st one equals the gob of rows in the 2nd one. (The pre-requisite in passage to be there able to multiply).<\p>

Up 2: Multiply the good weather of particular row of the first vein suitable for the initiation of each column in the sec matrix.<\p>

Step 3: Add the products.<\p>

P * Q= p(i decimeter j)*Q(k x veer) where j=k.<\p>

Generalized Pattern<\p>

If we numbers a 2€"3 matrix with a 3€"1 matrix, the product vein is 2€"1<\p>

Here is how we get M11 and M22 in the product.<\p>

M11 = r11€" t11 + r12€" t21 + r13€"t31 M12 = r21€" t11 + r22€" t21 + r23€"t31<\p>

In any matrix having one row and one columns then.<\p>

If a matrix having all content is zilch then its called zero matrix.<\p>

Present-day a matrix principle diagonal elements is coalesce(1) and other elements values is zeros then it is called as justice matrix.<\p>

In a country rock all upper transubstantiation in ideally solidus holy communion having non zeros and below are zeros then it is called as upper matrix.<\p>

In a matrix all lower elements in principle diagonal elements having non zeros and above are zeros earlier it is called thus lower chimney.<\p>

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C Program to Accept a Matrix of Order MxN & Interchange the Diagonals

/* * C program to accept a matrix of order M x N and store its elements * and interchange the main diagonal elements of the matrix * with that of the secondary diagonal elements */ #include <stdio.h>a void main () static int array[10][10]; int i, j, m, n, a; printf("Enter the order of the matix \n"); scanf("%d %d", &m, &n); if (m == n) printf("Enter the co-efficients of the matrix\n"); for (i = 0; i < m; ++i) for (j = 0; j < n; ++j) scanf("%dx%d", &array[i][j]); printf("The given matrix is \n"); for (i = 0; i < m; ++i) for (j = 0; j < n; ++j) printf(" %d", array[i][j]); printf("\n"); for (i = 0; i < m; ++i) a = array[i][i]; array[i][i] = array[i][m - i - 1]; array[i][m - i - 1] = a; printf("The matrix after changing the \n"); printf("main diagonal & secondary diagonal\n"); for (i = 0; i < m; ++i) for (j = 0; j < n; ++j) printf(" %d", array[i][j]); printf("\n"); else printf("The given order is not square matrix\n");

Output

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C program to find the sum of main diagonal and off diagonal elements of a matric

/* Write a C program to find accept a matric of order M x N and find the sum of the main diagonal and off diagonal elements */

#include <stdio.h> void main () { static int ma[10][10]; int i,j,m,n,a=0,sum=0; printf ("Enetr the order of the matix \n"); scanf ("%d %d",&m,&n); if ( m == n ) { printf ("Enter the co-efficients of the matrix\n"); for (i=0;i<m;++i) { for (j=0;j<n;++j) { scanf ("%d",&ma[i][j]); } } printf ("The given matrix is \n"); for (i=0;i<m;++i) { for (j=0;j<n;++j) { printf (" %d",ma[i][j]); } printf ("\n"); } for (i=0;i<m;++i) { sum = sum + ma[i][i]; a = a + ma[i][m-i-1]; } printf ("\nThe sum of the main diagonal elements is = %d\n",sum); printf ("The sum of the off diagonal elemets is = %d\n",a); } else printf ("The givan order is not square matrix\n"); }

Output

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C program to interchange the elements in multi dimensional matrix

/* Write a C program to accept a matrix of order M x N and store its elements  and interchange the main diagonal elements of the matrix with that of the secondary diagonal elements */

#include <stdio.h> void main () { static int ma[10][10]; int i,j,m,n,a; printf ("Enetr the order of the matix \n"); scanf ("%d %d",&m,&n); if (m ==n ) { printf ("Enter the co-efficients of the matrix\n"); for (i=0;i<m;++i) { for (j=0;j<n;++j) { scanf ("%dx%d",&ma[i][j]); } } printf ("The given matrix is \n"); for (i=0;i<m;++i) { for (j=0;j<n;++j) { printf (" %d",ma[i][j]); } printf ("\n"); } for (i=0;i<m;++i) { a = ma[i][i]; ma[i][i] = ma[i][m-i-1]; ma[i][m-i-1] = a; } printf ("THe matrix after changing the \n"); printf ("main diagonal & secondary diagonal\n"); for (i=0;i<m;++i) { for (j=0;j<n;++j) { printf (" %d",ma[i][j]); } printf ("\n"); } } else printf ("The givan order is not square matrix\n"); }

Output