Matrices Calculator – Loan calculator

Matrices Calculator (2×2)

Matrix A (2×2)

Matrix B (2×2)

Scalar (k)

Select Operation

Matrix A + Matrix B Matrix A – Matrix B k * Matrix A Matrix A * Matrix B Transpose Matrix A (A^T) Determinant of Matrix A (det(A))

Result:

.calculator-container { font-family: Arial, sans-serif; max-width: 600px; margin: 20px auto; padding: 20px; border: 1px solid #ccc; border-radius: 8px; background-color: #f9f9f9; } .matrix-input-section, .scalar-input-section, .operation-selection, .result-section { margin-bottom: 15px; padding: 10px; border: 1px solid #eee; border-radius: 5px; background-color: #fff; } .matrix-grid input { width: 50px; padding: 8px; margin: 5px; border: 1px solid #ddd; border-radius: 4px; text-align: center; } .matrix-grid { display: inline-block; /* To keep inputs aligned */ vertical-align: top; } select, button { padding: 10px 15px; margin-top: 10px; border: 1px solid #007bff; border-radius: 5px; background-color: #007bff; color: white; cursor: pointer; font-size: 16px; } select { background-color: #f0f0f0; color: #333; border: 1px solid #ccc; width: 100%; box-sizing: border-box; } button:hover { background-color: #0056b3; } .matrix-output { min-height: 50px; padding: 10px; border: 1px dashed #ccc; background-color: #e9e9e9; font-family: 'Courier New', Courier, monospace; white-space: pre; /* Preserve formatting for matrix display */ } h2, h3 { color: #333; } function getMatrix(prefix) { var m = []; for (var i = 1; i <= 2; i++) { var row = []; for (var j = 1; j <= 2; j++) { var id = prefix + i + j; var value = parseFloat(document.getElementById(id).value); if (isNaN(value)) { alert("Please enter valid numbers for all matrix elements."); return null; } row.push(value); } m.push(row); } return m; } function getScalar() { var scalar = parseFloat(document.getElementById("scalarK").value); if (isNaN(scalar)) { alert("Please enter a valid number for the scalar (k)."); return null; } return scalar; } function displayMatrix(matrix, targetId) { var resultDiv = document.getElementById(targetId); if (!matrix) { resultDiv.innerHTML = "Error: Invalid matrix."; return; } var html = ""; for (var i = 0; i < matrix.length; i++) { html += "[ "; for (var j = 0; j < matrix[i].length; j++) { html += matrix[i][j].toFixed(2) + (j < matrix[i].length – 1 ? ", " : ""); } html += " ]"; } resultDiv.innerHTML = html; } function displayScalar(scalar, targetId) { var resultDiv = document.getElementById(targetId); if (typeof scalar !== 'number' || isNaN(scalar)) { resultDiv.innerHTML = "Error: Invalid scalar result."; return; } resultDiv.innerHTML = scalar.toFixed(2); } function addMatrices(A, B) { var C = [[0, 0], [0, 0]]; for (var i = 0; i < 2; i++) { for (var j = 0; j < 2; j++) { C[i][j] = A[i][j] + B[i][j]; } } return C; } function subtractMatrices(A, B) { var C = [[0, 0], [0, 0]]; for (var i = 0; i < 2; i++) { for (var j = 0; j < 2; j++) { C[i][j] = A[i][j] – B[i][j]; } } return C; } function scalarMultiplyMatrix(k, A) { var C = [[0, 0], [0, 0]]; for (var i = 0; i < 2; i++) { for (var j = 0; j < 2; j++) { C[i][j] = k * A[i][j]; } } return C; } function multiplyMatrices(A, B) { var C = [[0, 0], [0, 0]]; C[0][0] = A[0][0] * B[0][0] + A[0][1] * B[1][0]; C[0][1] = A[0][0] * B[0][1] + A[0][1] * B[1][1]; C[1][0] = A[1][0] * B[0][0] + A[1][1] * B[1][0]; C[1][1] = A[1][0] * B[0][1] + A[1][1] * B[1][1]; return C; } function transposeMatrix(A) { var C = [[0, 0], [0, 0]]; C[0][0] = A[0][0]; C[0][1] = A[1][0]; C[1][0] = A[0][1]; C[1][1] = A[1][1]; return C; } function determinantMatrix(A) { return A[0][0] * A[1][1] – A[0][1] * A[1][0]; } function calculateMatrixOperation() { var operation = document.getElementById("matrixOperation").value; var matrixA = getMatrix("a"); var matrixB = getMatrix("b"); var scalar = getScalar(); var result; if (matrixA === null || (operation !== 'transposeA' && operation !== 'determinantA' && matrixB === null) || (operation === 'scalarMultiply' && scalar === null)) { document.getElementById("matrixResult").innerHTML = "Please ensure all required inputs are valid numbers."; return; } switch (operation) { case 'add': result = addMatrices(matrixA, matrixB); displayMatrix(result, "matrixResult"); break; case 'subtract': result = subtractMatrices(matrixA, matrixB); displayMatrix(result, "matrixResult"); break; case 'scalarMultiply': result = scalarMultiplyMatrix(scalar, matrixA); displayMatrix(result, "matrixResult"); break; case 'multiply': result = multiplyMatrices(matrixA, matrixB); displayMatrix(result, "matrixResult"); break; case 'transposeA': result = transposeMatrix(matrixA); displayMatrix(result, "matrixResult"); break; case 'determinantA': result = determinantMatrix(matrixA); displayScalar(result, "matrixResult"); break; default: document.getElementById("matrixResult").innerHTML = "Please select a valid operation."; } }

Understanding and Using the Matrices Calculator

Matrices are fundamental mathematical objects used to represent and manipulate data in various fields, including computer graphics, physics, engineering, economics, and data science. A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Each item in a matrix is called an element.

What is a Matrix?

A matrix is typically denoted by a capital letter (e.g., A, B) and its elements are enclosed in brackets. The size or 'order' of a matrix is defined by the number of its rows and columns (e.g., a 2×2 matrix has 2 rows and 2 columns). For example, a 2×2 matrix A looks like this:

    A = [ a₁₁  a₁₂ ]
        [ a₂₁  a₂₂ ]

Where a_ij refers to the element in the i-th row and j-th column.

Common Matrix Operations

Our calculator focuses on 2×2 matrices and supports several key operations:

1. Matrix Addition (A + B)

To add two matrices, they must have the same dimensions (same number of rows and columns). You add corresponding elements. If Matrix A = [[a, b], [c, d]] and Matrix B = [[e, f], [g, h]], then:

    A + B = [ a+e  b+f ]
            [ c+g  d+h ]

Example: If A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], then A + B = [[1+5, 2+6], [3+7, 4+8]] = [[6, 8], [10, 12]].

2. Matrix Subtraction (A – B)

Similar to addition, matrices must have the same dimensions. You subtract corresponding elements.

    A - B = [ a-e  b-f ]
            [ c-g  d-h ]

Example: If A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], then A – B = [[1-5, 2-6], [3-7, 4-8]] = [[-4, -4], [-4, -4]].

3. Scalar Multiplication (k * A)

Scalar multiplication involves multiplying every element of a matrix by a single number (scalar). If k is a scalar and A = [[a, b], [c, d]], then:

    k * A = [ k*a  k*b ]
            [ k*c  k*d ]

Example: If k = 2 and A = [[1, 2], [3, 4]], then 2 * A = [[2*1, 2*2], [2*3, 2*4]] = [[2, 4], [6, 8]].

4. Matrix Multiplication (A * B)

Matrix multiplication is more complex. 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. For 2×2 matrices, A = [[a, b], [c, d]] and B = [[e, f], [g, h]]:

    A * B = [ (a*e + b*g)  (a*f + b*h) ]
            [ (c*e + d*g)  (c*f + d*h) ]

Example: If A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], then A * B = [[(1*5 + 2*7), (1*6 + 2*8)], [(3*5 + 4*7), (3*6 + 4*8)]] = [[(5+14), (6+16)], [(15+28), (18+32)]] = [[19, 22], [43, 50]].

5. Transpose of a Matrix (A^T)

The transpose of a matrix is obtained by swapping its rows and columns. The rows of the original matrix become the columns of the transposed matrix, and vice-versa. If A = [[a, b], [c, d]], then:

    A^T = [ a  c ]
            [ b  d ]

Example: If A = [[1, 2], [3, 4]], then A^T = [[1, 3], [2, 4]].

6. Determinant of a Matrix (det(A))

The determinant is a scalar value that can be computed from the elements of a square matrix. It provides important information about the matrix, such as whether it is invertible. For a 2×2 matrix A = [[a, b], [c, d]], the determinant is calculated as:

    det(A) = (a * d) - (b * c)

Example: If A = [[1, 2], [3, 4]], then det(A) = (1 * 4) – (2 * 3) = 4 – 6 = -2.

How to Use This Calculator

Input Matrices: Enter the numerical values for Matrix A and Matrix B into the respective 2×2 grids. Default values are provided for quick testing.
Input Scalar: If you plan to perform scalar multiplication, enter your desired scalar value (k) in the "Scalar (k)" field.
Select Operation: Choose the desired matrix operation from the dropdown menu.
Calculate: Click the "Calculate" button to see the result.
View Result: The calculated matrix or scalar determinant will be displayed in the "Result" area.

This calculator is a handy tool for quickly performing common operations on 2×2 matrices, helping you verify your manual calculations or explore matrix properties.