neve domain was triggered too early. This is usually an indicator for some code in the plugin or theme running too early. Translations should be loaded at the init action or later. Please see Debugging in WordPress for more information. (This message was added in version 6.7.0.) in /home/mathze5/public_html/learnermath.com/wp-includes/functions.php on line 6114When we want to add and subtract matrices together, each matrix has to be the same size.\n When multiplying a matrix by a single number, all we need to do is multiply each matrix element by that number.\n
\nSo they need to have the same number of rows and the same number of columns.\n
\nA 3 × 3 matrix would have to be added to or subtracted from another 3 × 3 matrix.\n
\nWe just add together the equivalent matrix elements.<\/p>\n
\n \\begin{bmatrix} a_{11} & a_{12} & a_{13} \\\\ a_{21} & a_{22} & a_{23} \\\\ a_{31} & a_{32} & a_{33} \\end{bmatrix}<\/span> +<\/font> \\begin{bmatrix} b_{11} & b_{12} & b_{13} \\\\ b_{21} & b_{22} & b_{23} \\\\ b_{31} & b_{32} & b_{33} \\end{bmatrix}<\/span>\n
\n= \\begin{bmatrix} a_{11}+b_{11} & a_{12}+b_{12} & a_{13}+b_{13} \\\\ a_{21}+b_{21} & a_{22}+b_{22} & a_{23}+b_{23} \\\\ a_{31}+b_{31} & a_{32}+b_{32} & a_{33}+b_{33} \\end{bmatrix}<\/span>\n
\nThe same goes for matrix subtraction, it’s the same approach when we add and subtract matrices.\n
\n<\/a>\n\n\n\nAdd and Subtract Matrices Examples<\/span><\/h2>\n\n\n\n
\n(1.1) <\/i><\/b><\/font><\/u><\/font><\/font>\n
\n\\begin{bmatrix} 1 & 2 & 4 \\\\ 3 & 1 & 8 \\end{bmatrix}<\/span> +<\/font> \\begin{bmatrix} 5 & 6 & 7 \\\\ 4 & 1 & 1 \\end{bmatrix}<\/span>\n
\n= \\begin{bmatrix} 1+5 & 2+6 & 4+7 \\\\ 3+4 & 1+1 & 8+1 \\end{bmatrix}<\/span> = \\begin{bmatrix} 6 & 8 & 11 \\\\ 7 & 2 & 9 \\end{bmatrix}<\/span>\n
\n(1.2) <\/i><\/b><\/font><\/u><\/font><\/font>\n
\n\\begin{bmatrix} 3 & 2 & 1 \\\\ 4 & 4 & 2 \\\\ 9 & 8 & 6 \\end{bmatrix}<\/span> −<\/font> \\begin{bmatrix} 1 & 1 & 2 \\\\ 2 & 3 & 1 \\\\ 7 & 5 & 4 \\end{bmatrix}<\/span>\n
\n= \\begin{bmatrix} 3-1 & 2-1 & 1-2 \\\\ 4-2 & 4-3 & 2-1 \\\\ 9-7 & 8-5 & 6-4 \\end{bmatrix}<\/span> = \\begin{bmatrix} 2 & 1 & {\\text{-}}1 \\\\ 2 & 1 & 1 \\\\ 2 & 3 & 2 \\end{bmatrix}<\/span>\n
\n(1.3) <\/i><\/b><\/font><\/u><\/font><\/font>\n
\n\\begin{bmatrix} {\\text{-}}1 & 3 \\\\ 4 & {\\text{-}}9 \\\\ 2 & 7 \\end{bmatrix}<\/span> +<\/font> \\begin{bmatrix} {\\text{-}}2 & 1 \\\\ 3 & 0 \\\\ 1 & 2 \\end{bmatrix}<\/span>\n
\n= \\begin{bmatrix} {\\text{-}}1+{\\text{-}}2 & 3+1 \\\\ 4+3 & 3+0 \\\\ 2+1 & 7+2 \\end{bmatrix}<\/span> = \\begin{bmatrix} {\\text{-}}3 & 4 \\\\ 7 & 3 \\\\ 3 & 9 \\end{bmatrix}<\/span>\n
\n(1.4) <\/i><\/b><\/font><\/u><\/font><\/font>\n
\n\\begin{bmatrix} {\\text{-}}2 & 5 & 4 \\\\ 0 & {\\text{-}}2 & 6 \\end{bmatrix}<\/span> −<\/font> \\begin{bmatrix} {\\text{-}}4 & 3 & 1 \\\\ {\\text{-}}1 & {\\text{-}}7 & 9 \\end{bmatrix}<\/span>\n
\n= \\begin{bmatrix} {\\text{-}}2-{\\text{-}}4 & 5-3 & 4-1 \\\\ 0-{\\text{-}}1 & {\\text{-}}2-{\\text{-}}7 & 6-9 \\end{bmatrix}<\/span>\n
\n= \\begin{bmatrix} 2 & 2 & 3 \\\\ 1 & 5 & {\\text{-}}3 \\end{bmatrix}<\/span>\n
\n<\/a>\n\n\n\n
\n\n\n\nMultiplying a Matrix by a Number<\/span><\/h2>\n\n\n\n
\n
\nThe matrix itself stays the same size with the same number of rows and columns.<\/p>\n
\nExamples <\/u><\/font><\/font><\/font><\/b>\n
\n(2.1) <\/i><\/b><\/font><\/u><\/font><\/font>\n
\n3<\/font> × \\begin{bmatrix} 4 & 1 & 2 \\\\ 3 & 5 & 1 \\end{bmatrix}<\/span> = \\begin{bmatrix} 3\\times4 & 3\\times1 & 3\\times2 \\\\ 3\\times3 & 3\\times5 & 3\\times1 \\end{bmatrix}<\/span> = \\begin{bmatrix} 12 & 3 & 6 \\\\ 9 & 15 & 3 \\end{bmatrix}<\/span>\n
\n(2.2) <\/i><\/b><\/font><\/u><\/font><\/font>\n
\n–2<\/font> × \\begin{bmatrix} {\\text{-}}1 & 4 \\\\ 7 & {\\text{-}}3 \\\\ 0 & 8 \\end{bmatrix}<\/span> = \\begin{bmatrix} {\\text{-}}2\\times1 & {\\text{-}}2\\times4 \\\\ {\\text{-}}2\\times7 & {\\text{-}}2\\times{\\text{-}}3 \\\\ {\\text{-}}2\\times0 & {\\text{-}}2\\times8 \\end{bmatrix}<\/span>\n
\n= \\begin{bmatrix} {\\text{-}}2 & {\\text{-}}8 \\\\ {\\text{-}}14 & 6 \\\\ 0 & {\\text{-}}16 \\end{bmatrix}<\/span>\n
\n\n\n