This Matrix Transpose calculator reads the matrix size, then the matrix of specified size from user, and then finds the transpose of the matrix, with a step by step solution.
Examples to use Matrix Transpose Calculator
1. Find the transpose of the following 3×3 matrix.
{
"topic": "matrix-transpose",
"title": "Matrix Transpose Calculator",
"tag": "Matrix",
"template": "matrix",
"n_matrices": 1,
"different_size": false,
"symbol": "",
"description": "This Matrix Transpose calculator reads the matrix size, then the matrix of specified size from user, and then finds the transpose of the matrix, with a step by step solution.",
"content": "<div class=\"flex_row\"><div class=\"input_section\"><form onsubmit=\"return calculate()\"><div style=\"padding:10px\"><h3>Enter Matrix Size</h3><div id=\"matrix_size\"><input type=\"number\" required step=\"1\" min=\"1\" id=\"a_m\" name=\"a_m\" value=\"\" placeholder=\"m\" /> × <input type=\"number\" required step=\"1\" min=\"1\" id=\"a_n\" name=\"a_n\" value=\"\" placeholder=\"n\" /><p id=\"entry_msg\" class=\"warning\"></p></div><h3>Enter matrix <strong>A</strong></h3><div id=\"m_a\"><p class=\"hint\">The matrix appears when you enter the size: m, n.</p></div></div><button type=\"submit\" class=\"calculate primary_action\"\">Calculate</button></form></div></div><div id=\"solution\"></div><button onclick=\"printContent()\" class=\"noprint print_button\">Print</button><h2>Examples to use Matrix Transpose Calculator</h2><h3 class=\"example\"><span class=\"example_number\">1.</span> Find the transpose of the following 3×3 matrix.</h3><p>Matrix <span>\\({\\ A = \\begin{bmatrix}1 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{bmatrix} }\\)</span></p><h3 class=\"solution\">Solution</h3><div class=\"solution\"><p>Since the given matrix is of size 3×3, follow these steps with the Matrix Transpose Calculator.<ol><li>Enter matrix size of 3×3 in input fields: <span class=\"strong\">m=3</span> and <span class=\"strong\">n=3</span>.</li><li>A matrix with specified size of 3×3 appears, with input field for each element in the matrix.</li><li>Enter the given matrix values, and click on Calculate button.</li><li>A step-by-step solution with the following steps will be displayed.</li></ol></p><p class=\"strong\">Given:</p><p class=\"step\">Matrix \\( A = \\begin{bmatrix}1 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{bmatrix} \\)</p><p class=\"strong\">Computing Matrix Transpose:\\( A^T \\)</p><p>Convert the rows of given matrix \\( A \\) to the columns.</p><p class=\"step\">\\( A^T = \\begin{bmatrix}1 & 4 & 7\\\\2 & 5 & 8\\\\3 & 6 & 9\\end{bmatrix} \\)</p><p class=\"strong\">Result</p><p>The transpose of the matrix A is</p><p class=\"board color1\">\\( A^T = \\begin{bmatrix}1 & 4 & 7\\\\2 & 5 & 8\\\\3 & 6 & 9\\end{bmatrix} \\)</p></div><h3 class=\"example\"><span class=\"example_number\">2.</span> Find the transpose of the following 2×4 matrix.</h3><p>Matrix <span>\\({\\ A = \\begin{bmatrix}1 & 2 & 3 & 4\\\\5 & 6 & 7 & 8\\end{bmatrix} }\\)</span></p><h3 class=\"solution\">Solution</h3><div class=\"solution\"><p>Since the given matrix is of size 2×4, follow these steps with the Matrix Transpose Calculator.<ol><li>Enter matrix size of 2×4 in input fields: <span class=\"strong\">m=2</span> and <span class=\"strong\">n=4</span>.</li><li>A matrix with specified size of 3×3 appears, with input field for each element in the matrix.</li><li>Enter the given matrix values, and click on Calculate button.</li><li>A step-by-step solution with the following steps will be displayed.</li></ol></p><p class=\"strong\">Given:</p><p class=\"step\">Matrix \\( A = \\begin{bmatrix}1 & 2 & 3 & 4\\\\5 & 6 & 7 & 8\\end{bmatrix} \\)</p><p class=\"strong\">Computing Matrix Transpose:\\( A^T \\)</p><p>Convert the rows of given matrix \\( A \\) to the columns.</p><p class=\"step\">\\( A^T = \\begin{bmatrix}1 & 5\\\\2 & 6\\\\3 & 7\\\\4 & 8\\end{bmatrix} \\)</p><p class=\"strong\">Result</p><p>The transpose of the matrix A is</p><p class=\"board color1\">\\( A^T = \\begin{bmatrix}1 & 5\\\\2 & 6\\\\3 & 7\\\\4 & 8\\end{bmatrix} \\)</p></div>",
"links": [
[
"Matrix Addition Calculator",
"/calculators/algebra/matrices/matrix-addition"
],
[
"Matrix Subtraction Calculator",
"/calculators/algebra/matrices/matrix-subtraction"
],
[
"Matrix Multiplication Calculator",
"/calculators/algebra/matrices/matrix-multiplication"
],
[
"Matrix Transpose Calculator",
"/calculators/algebra/matrices/matrix-transpose"
],
[
"Matrix Inverse Calculator",
"/calculators/algebra/matrices/matrix-inverse"
],
[
"Matrix Determinant Calculator",
"/calculators/algebra/matrices/matrix-determinant"
],
[
"Matrix Rank Calculator",
"/calculators/algebra/matrices/matrix-rank"
],
[
"Cofactor Matrix Calculator",
"/calculators/algebra/matrices/matrix-cofactor"
],
[
"Adjoint Matrix Calculator",
"/calculators/algebra/matrices/matrix-adjoint"
]
]
}
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