.calculator-container {
font-family: Arial, sans-serif;
max-width: 700px;
margin: 20px auto;
padding: 20px;
border: 1px solid #ccc;
border-radius: 8px;
background-color: #f9f9f9;
}
.calculator-container h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
}
.calculator-container p {
margin-bottom: 15px;
line-height: 1.6;
}
.input-group {
margin-bottom: 15px;
}
.input-group label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.input-group textarea,
.input-group input[type="number"],
.input-group select {
width: calc(100% – 12px);
padding: 8px;
border: 1px solid #ddd;
border-radius: 4px;
box-sizing: border-box;
}
.input-group textarea {
resize: vertical;
}
.calculator-container button {
display: block;
width: 100%;
padding: 10px 15px;
background-color: #007bff;
color: white;
border: none;
border-radius: 4px;
font-size: 16px;
cursor: pointer;
transition: background-color 0.3s ease;
}
.calculator-container button:hover {
background-color: #0056b3;
}
.calculator-result {
margin-top: 20px;
padding: 15px;
border: 1px solid #e0e0e0;
border-radius: 4px;
background-color: #e9ecef;
min-height: 50px;
color: #333;
}
.calculator-result h3 {
margin-top: 0;
color: #007bff;
}
.matrix-table {
border-collapse: collapse;
margin-top: 10px;
width: auto; /* Adjust width based on content */
}
.matrix-table td {
border: 1px solid #ccc;
padding: 8px 12px;
text-align: center;
min-width: 40px;
}
function parseMatrix(matrixString) {
var rows = matrixString.trim().split('\n');
var matrix = [];
var numCols = -1;
if (matrixString.trim() === "") {
return null; // Indicate empty matrix
}
for (var i = 0; i < rows.length; i++) {
var row = rows[i].trim();
if (row === "") continue; // Skip empty rows
// Split by space or comma, then filter out empty strings
var elements = row.split(/[\s,]+/).filter(function(el) { return el !== ''; });
var parsedRow = [];
if (elements.length === 0) {
return null; // Row with no elements
}
for (var j = 0; j < elements.length; j++) {
var num = parseFloat(elements[j]);
if (isNaN(num)) {
return null; // Invalid number found
}
parsedRow.push(num);
}
if (numCols === -1) {
numCols = parsedRow.length;
} else if (parsedRow.length !== numCols) {
return null; // Inconsistent number of columns
}
matrix.push(parsedRow);
}
if (matrix.length === 0) return null; // No valid rows parsed
return matrix;
}
function displayMatrix(matrix, title) {
if (!matrix || matrix.length === 0 || matrix[0].length === 0) {
return "
";
return html;
}
function addMatrices(matrixA, matrixB) {
if (!matrixA || !matrixB || matrixA.length === 0 || matrixB.length === 0 ||
matrixA.length !== matrixB.length || matrixA[0].length !== matrixB[0].length) {
return "Error: Matrices must have the same dimensions for addition.";
}
var result = [];
for (var i = 0; i < matrixA.length; i++) {
result.push([]);
for (var j = 0; j < matrixA[0].length; j++) {
result[i].push(matrixA[i][j] + matrixB[i][j]);
}
}
return result;
}
function subtractMatrices(matrixA, matrixB) {
if (!matrixA || !matrixB || matrixA.length === 0 || matrixB.length === 0 ||
matrixA.length !== matrixB.length || matrixA[0].length !== matrixB[0].length) {
return "Error: Matrices must have the same dimensions for subtraction.";
}
var result = [];
for (var i = 0; i < matrixA.length; i++) {
result.push([]);
for (var j = 0; j < matrixA[0].length; j++) {
result[i].push(matrixA[i][j] – matrixB[i][j]);
}
}
return result;
}
function multiplyMatrices(matrixA, matrixB) {
if (!matrixA || !matrixB || matrixA.length === 0 || matrixB.length === 0 ||
matrixA[0].length !== matrixB.length) {
return "Error: Number of columns in Matrix A must equal number of rows in Matrix B for multiplication.";
}
var rowsA = matrixA.length;
var colsA = matrixA[0].length;
var rowsB = matrixB.length;
var colsB = matrixB[0].length;
var result = [];
for (var i = 0; i < rowsA; i++) {
result[i] = [];
for (var j = 0; j < colsB; j++) {
var sum = 0;
for (var k = 0; k < colsA; k++) { // or rowsB, they are equal
sum += matrixA[i][k] * matrixB[k][j];
}
result[i][j] = sum;
}
}
return result;
}
function scalarMultiply(matrix, scalar) {
if (!matrix || matrix.length === 0 || matrix[0].length === 0) {
return "Error: Cannot perform scalar multiplication on an empty or invalid matrix.";
}
var result = [];
for (var i = 0; i < matrix.length; i++) {
result.push([]);
for (var j = 0; j < matrix[i].length; j++) {
result[i].push(matrix[i][j] * scalar);
}
}
return result;
}
function transposeMatrix(matrix) {
if (!matrix || matrix.length === 0 || matrix[0].length === 0) {
return "Error: Cannot transpose an empty or invalid matrix.";
}
var rows = matrix.length;
var cols = matrix[0].length;
var result = [];
for (var j = 0; j < cols; j++) {
result[j] = [];
for (var i = 0; i < rows; i++) {
result[j][i] = matrix[i][j];
}
}
return result;
}
function calculateMatrix() {
var matrixAString = document.getElementById('matrixAInput').value;
var matrixBString = document.getElementById('matrixBInput').value;
var scalarValueString = document.getElementById('scalarInput').value;
var operation = document.getElementById('operationSelect').value;
var resultDiv = document.getElementById('result');
resultDiv.innerHTML = ''; // Clear previous results
var matrixA = parseMatrix(matrixAString);
var matrixB = parseMatrix(matrixBString);
var scalar = parseFloat(scalarValueString);
if (isNaN(scalar)) {
resultDiv.innerHTML = "Error: Invalid scalar value. Please enter a number.";
return;
}
var calculationResult;
var error = false;
switch (operation) {
case 'add':
if (!matrixA) { resultDiv.innerHTML = "Error: Matrix A is empty or invalid."; return; }
if (!matrixB) { resultDiv.innerHTML = "Error: Matrix B is empty or invalid."; return; }
calculationResult = addMatrices(matrixA, matrixB);
break;
case 'subtract':
if (!matrixA) { resultDiv.innerHTML = "Error: Matrix A is empty or invalid."; return; }
if (!matrixB) { resultDiv.innerHTML = "Error: Matrix B is empty or invalid."; return; }
calculationResult = subtractMatrices(matrixA, matrixB);
break;
case 'multiply':
if (!matrixA) { resultDiv.innerHTML = "Error: Matrix A is empty or invalid."; return; }
if (!matrixB) { resultDiv.innerHTML = "Error: Matrix B is empty or invalid."; return; }
calculationResult = multiplyMatrices(matrixA, matrixB);
break;
case 'scalarMultiplyA':
if (!matrixA) { resultDiv.innerHTML = "Error: Matrix A is empty or invalid."; return; }
calculationResult = scalarMultiply(matrixA, scalar);
break;
case 'scalarMultiplyB':
if (!matrixB) { resultDiv.innerHTML = "Error: Matrix B is empty or invalid."; return; }
calculationResult = scalarMultiply(matrixB, scalar);
break;
case 'transposeA':
if (!matrixA) { resultDiv.innerHTML = "Error: Matrix A is empty or invalid."; return; }
calculationResult = transposeMatrix(matrixA);
break;
case 'transposeB':
if (!matrixB) { resultDiv.innerHTML = "Error: Matrix B is empty or invalid."; return; }
calculationResult = transposeMatrix(matrixB);
break;
default:
resultDiv.innerHTML = "Error: Unknown operation selected.";
return;
}
if (typeof calculationResult === 'string') {
resultDiv.innerHTML = "" + calculationResult + "";
} else {
resultDiv.innerHTML = displayMatrix(calculationResult, "Resulting Matrix");
}
}
Understanding Matrices and Their Operations
Matrices are fundamental mathematical objects used to represent and manipulate data in various fields, including physics, engineering, computer graphics, economics, and statistics. A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The size or dimension of a matrix is defined by the number of rows (m) and columns (n) it has, denoted as m x n.
What is a Matrix?
Imagine a spreadsheet. That's essentially a matrix! Each cell contains a value, and these values are organized by their row and column position. For example, a 2×3 matrix has 2 rows and 3 columns:
A = [ a₁₁ a₁₂ a₁₃ ]
[ a₂₁ a₂₂ a₂₃ ]
Where aᵢⱼ refers to the element in the i-th row and j-th column.
Common Matrix Operations
Our Matrix Calculator allows you to perform several essential operations:
1. Matrix Addition and Subtraction
To add or subtract two matrices, they must have the exact same dimensions (same number of rows and same number of columns). The operation is performed element-wise: you add or subtract corresponding elements from each matrix to get the corresponding element in the result matrix.
Example:
A = [ 1 2 ] B = [ 5 6 ]
[ 3 4 ] [ 7 8 ]
A + B = [ (1+5) (2+6) ] = [ 6 8 ]
[ (3+7) (4+8) ] [ 10 12 ]
A - B = [ (1-5) (2-6) ] = [ -4 -4 ]
[ (3-7) (4-8) ] [ -4 -4 ]
Using the calculator, input Matrix A as "1 2\n3 4" and Matrix B as "5 6\n7 8", then select "Matrix A + Matrix B" or "Matrix A – Matrix B".
2. Scalar Multiplication
Scalar multiplication involves multiplying every element of a matrix by a single number (a scalar). This operation changes the magnitude of the matrix elements but not its dimensions.
Example:
A = [ 1 2 ] Scalar (k) = 2
[ 3 4 ]
k * A = [ (2*1) (2*2) ] = [ 2 4 ]
[ (2*3) (2*4) ] [ 6 8 ]
Using the calculator, input Matrix A as "1 2\n3 4", Scalar Value as "2", then select "Scalar * Matrix A".
3. Matrix Multiplication
Matrix multiplication is more complex than scalar multiplication. For two matrices A (m x n) and B (p x q) to be multiplied, the number of columns in A must equal the number of rows in B (i.e., n = p). The resulting matrix C will have dimensions m x q.
Each element Cᵢⱼ of the product matrix is obtained by taking the dot product of the i-th row of A and the j-th column of B.
Example:
A = [ 1 2 ] (2x2) B = [ 5 6 ] (2x2)
[ 3 4 ] [ 7 8 ]
A * B = [ (1*5 + 2*7) (1*6 + 2*8) ] = [ (5+14) (6+16) ] = [ 19 22 ]
[ (3*5 + 4*7) (3*6 + 4*8) ] [ (15+28) (18+32) ] [ 43 50 ]
Using the calculator, input Matrix A as "1 2\n3 4" and Matrix B as "5 6\n7 8", then select "Matrix A * Matrix B".
4. Transpose of a Matrix
The transpose of a matrix (denoted Aᵀ) is obtained by flipping the matrix over its diagonal, meaning rows become columns and columns become rows. If A is an m x n matrix, its transpose Aᵀ will be an n x m matrix.
Example:
A = [ 1 2 3 ] (2x3)
[ 4 5 6 ]
Aᵀ = [ 1 4 ] (3x2)
[ 2 5 ]
[ 3 6 ]
Using the calculator, input Matrix A as "1 2 3\n4 5 6", then select "Transpose Matrix A".
How to Use the Calculator
- Enter Matrix A and Matrix B: Type the elements of your matrices into the respective text areas. Separate numbers in a row with spaces or commas, and use a new line for each new row.
- Enter Scalar Value: If you plan to perform scalar multiplication, enter the scalar number in the designated input field.
- Select Operation: Choose the desired matrix operation from the dropdown menu.
- Click "Calculate": The result will be displayed below, showing the resulting matrix.
This calculator is a handy tool for students, engineers, and anyone working with linear algebra, providing quick and accurate results for common matrix manipulations.