Adding matrices of random size: two to four rows and two to four columns. Advice (i.e. solution) has conditional visibility to show only the correct size.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "We can add any two matrices which have the same size. To add the matrices, we add each entry separately: entry 1,1 of the first matrix plus entry 1,1 of the second matrix goes into entry 1,1 of the sum, and so on.
\n\\[\\var{matrixA}+\\var{matrixB}= \\begin{pmatrix} \\simplify[]{{matrixA[0][0]}+{matrixB[0][0]}}&\\simplify[]{{matrixA[0][1]}+{matrixB[0][1]}}\\\\\\simplify[]{{matrixA[1][0]}+{matrixB[1][0]}} & \\simplify[]{{matrixA[1][1]}+{matrixB[1][1]}}\\end{pmatrix}=\\var{matrixC}\\]
\n\\[\\var{matrixA}+\\var{matrixB}= \\begin{pmatrix} \\simplify[]{{matrixA[0][0]}+{matrixB[0][0]}}&\\simplify[]{{matrixA[0][1]}+{matrixB[0][1]}} &\\simplify[]{{matrixA[0][2]}+{matrixB[0][2]}} \\\\\\simplify[]{{matrixA[1][0]}+{matrixB[1][0]}} & \\simplify[]{{matrixA[1][1]}+{matrixB[1][1]}}&\\simplify[]{{matrixA[1][2]}+{matrixB[1][2]}}\\end{pmatrix}=\\var{matrixC}\\]
\n\\[\\var{matrixA}+\\var{matrixB}= \\begin{pmatrix} \\simplify[]{{matrixA[0][0]}+{matrixB[0][0]}}&\\simplify[]{{matrixA[0][1]}+{matrixB[0][1]}} &\\simplify[]{{matrixA[0][2]}+{matrixB[0][2]}} &\\simplify[]{{matrixA[0][3]}+{matrixB[0][3]}}\\\\\\simplify[]{{matrixA[1][0]}+{matrixB[1][0]}} & \\simplify[]{{matrixA[1][1]}+{matrixB[1][1]}}&\\simplify[]{{matrixA[1][2]}+{matrixB[1][2]}} &\\simplify[]{{matrixA[1][3]}+{matrixB[1][3]}}\\end{pmatrix}=\\var{matrixC}\\]
\n\\[\\var{matrixA}+\\var{matrixB}= \\begin{pmatrix} \\simplify[]{{matrixA[0][0]}+{matrixB[0][0]}}&\\simplify[]{{matrixA[0][1]}+{matrixB[0][1]}} \\\\\\simplify[]{{matrixA[1][0]}+{matrixB[1][0]}} & \\simplify[]{{matrixA[1][1]}+{matrixB[1][1]}}\\\\\\simplify[]{{matrixA[2][0]}+{matrixB[2][0]}} & \\simplify[]{{matrixA[2][1]}+{matrixB[2][1]}}\\end{pmatrix}=\\var{matrixC}\\]
\n\\[\\var{matrixA}+\\var{matrixB}= \\begin{pmatrix} \\simplify[]{{matrixA[0][0]}+{matrixB[0][0]}}&\\simplify[]{{matrixA[0][1]}+{matrixB[0][1]}} &\\simplify[]{{matrixA[0][2]}+{matrixB[0][2]}} \\\\\\simplify[]{{matrixA[1][0]}+{matrixB[1][0]}} & \\simplify[]{{matrixA[1][1]}+{matrixB[1][1]}}&\\simplify[]{{matrixA[1][2]}+{matrixB[1][2]}} \\\\\\simplify[]{{matrixA[2][0]}+{matrixB[2][0]}} & \\simplify[]{{matrixA[2][1]}+{matrixB[2][1]}}&\\simplify[]{{matrixA[2][2]}+{matrixB[2][2]}} \\end{pmatrix}=\\var{matrixC}\\]
\n\\[\\var{matrixA}+\\var{matrixB}= \\begin{pmatrix} \\simplify[]{{matrixA[0][0]}+{matrixB[0][0]}}&\\simplify[]{{matrixA[0][1]}+{matrixB[0][1]}} &\\simplify[]{{matrixA[0][2]}+{matrixB[0][2]}} &\\simplify[]{{matrixA[0][3]}+{matrixB[0][3]}}\\\\\\simplify[]{{matrixA[1][0]}+{matrixB[1][0]}} & \\simplify[]{{matrixA[1][1]}+{matrixB[1][1]}}&\\simplify[]{{matrixA[1][2]}+{matrixB[1][2]}} &\\simplify[]{{matrixA[1][3]}+{matrixB[1][3]}}\\\\\\simplify[]{{matrixA[2][0]}+{matrixB[2][0]}} & \\simplify[]{{matrixA[2][1]}+{matrixB[2][1]}}&\\simplify[]{{matrixA[2][2]}+{matrixB[2][2]}} &\\simplify[]{{matrixA[2][3]}+{matrixB[2][3]}}\\end{pmatrix}=\\var{matrixC}\\]
\n\\[\\var{matrixA}+\\var{matrixB}= \\begin{pmatrix} \\simplify[]{{matrixA[0][0]}+{matrixB[0][0]}}&\\simplify[]{{matrixA[0][1]}+{matrixB[0][1]}} \\\\ \\simplify[]{{matrixA[1][0]}+{matrixB[1][0]}} & \\simplify[]{{matrixA[1][1]}+{matrixB[1][1]}}\\\\\\simplify[]{{matrixA[2][0]}+{matrixB[2][0]}} & \\simplify[]{{matrixA[2][1]}+{matrixB[2][1]}}\\\\\\simplify[]{{matrixA[3][0]}+{matrixB[3][0]}} & \\simplify[]{{matrixA[3][1]}+{matrixB[3][1]}}\\end{pmatrix}=\\var{matrixC}\\]
\n\\[\\var{matrixA}+\\var{matrixB}= \\begin{pmatrix} \\simplify[]{{matrixA[0][0]}+{matrixB[0][0]}}&\\simplify[]{{matrixA[0][1]}+{matrixB[0][1]}} &\\simplify[]{{matrixA[0][2]}+{matrixB[0][2]}} \\\\\\simplify[]{{matrixA[1][0]}+{matrixB[1][0]}} & \\simplify[]{{matrixA[1][1]}+{matrixB[1][1]}}&\\simplify[]{{matrixA[1][2]}+{matrixB[1][2]}} \\\\\\simplify[]{{matrixA[2][0]}+{matrixB[2][0]}} & \\simplify[]{{matrixA[2][1]}+{matrixB[2][1]}}&\\simplify[]{{matrixA[2][2]}+{matrixB[2][2]}} \\\\\\simplify[]{{matrixA[3][0]}+{matrixB[3][0]}} & \\simplify[]{{matrixA[3][1]}+{matrixB[3][1]}}&\\simplify[]{{matrixA[3][2]}+{matrixB[3][2]}} \\end{pmatrix}=\\var{matrixC}\\]
\n\\[\\var{matrixA}+\\var{matrixB}= \\begin{pmatrix} \\simplify[]{{matrixA[0][0]}+{matrixB[0][0]}}&\\simplify[]{{matrixA[0][1]}+{matrixB[0][1]}} &\\simplify[]{{matrixA[0][2]}+{matrixB[0][2]}} &\\simplify[]{{matrixA[0][3]}+{matrixB[0][3]}}\\\\\\simplify[]{{matrixA[1][0]}+{matrixB[1][0]}} & \\simplify[]{{matrixA[1][1]}+{matrixB[1][1]}}&\\simplify[]{{matrixA[1][2]}+{matrixB[1][2]}} &\\simplify[]{{matrixA[1][3]}+{matrixB[1][3]}}\\\\\\simplify[]{{matrixA[2][0]}+{matrixB[2][0]}} & \\simplify[]{{matrixA[2][1]}+{matrixB[2][1]}}&\\simplify[]{{matrixA[2][2]}+{matrixB[2][2]}} &\\simplify[]{{matrixA[2][3]}+{matrixB[2][3]}}\\\\\\simplify[]{{matrixA[3][0]}+{matrixB[3][0]}} & \\simplify[]{{matrixA[3][1]}+{matrixB[3][1]}}&\\simplify[]{{matrixA[3][2]}+{matrixB[3][2]}} &\\simplify[]{{matrixA[3][3]}+{matrixB[3][3]}}\\end{pmatrix}=\\var{matrixC}\\]
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