7.3.26 (Write sim. eqns. with matrices) (presentation teaching copy) Write the following system of linear equations as a matrix equation. \[ \begin{align*} &{@a1@}x_1 + {@a2@}x_2 + {@a3@}x_3 = {@b1@} \\ &{@a4@}x_1 + {@a5@}x_2 + {@a6@}x_3 = {@b2@} \\ &{@a7@}x_1 + {@a8@}x_2 + {@a9@}x_3 = {@b3@} \end{align*} \]

• [[input:ans1]] [[validation:ans1]] \(\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \)[[input:ans2]] [[validation:ans2]]

]]> We can use matrices to write this equation in the form \(A \mathbf{x} = \mathbf{b}\). So the coefficients of each \(x_i\) are the entries of the matrix \(A\) and the entries of the vector \(\mathbf{b}\) are the values on the right hand side of the equals sign. So we have \[ {@ta1@} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = {@ta2@}. \]

]]> 1 0.1 0 2020081700 a1: 1+rand(5); a2: 1+rand(5); a3: 1+rand(5); a4: 1+rand(5); a5: 1+rand(5); a6: 1+rand(5); a7: 1+rand(5); a8: 1+rand(5); a9: 1+rand(5); b1: 1+rand(10); b2: 1+rand(10); b3: 1+rand(10); ta1: matrix([a1,a2,a3],[a4,a5,a6],[a7,a8,a9]); ta2: matrix([b1],[b2],[b3]); [[feedback:prt1]] \({@ta1@} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} {@ta2@}\) 1 0 0 *10 dot 1 i cos-1 lang [ 0 {"author":[{"firstName":"","lastName":"","institution":"Unknown - Legacy question","year":"2025"}],"language":["en"],"isPartOf":"STACK Library","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}} ans1 matrix ta1 5 1 0 0 1 0 0 1 3 ans2 matrix ta2 5 1 0 0 1 0 0 1 3 prt1 1.0000000 1 1 0 AlgEquiv ans1 ta1 0 = 0.5000000 1 prt1-1-T = 0.0000000 1 prt1-1-F 1 AlgEquiv ans2 ta2 0 + 0.5000000 -1 prt1-2-T - 0.0000000 -1 prt1-2-F 1930245414 812684119 1827462946 145180072 36715103 946761244 1804442351 851490863 2007618713 856928557 892429656 1685384646 1559087057 747596696 1509610601 40582546 601565325 1184321902 997386553 2017829241 1670848744 1535580682 3390270 1021119565 2020613490 1564017995 2091565715 233658395 1275737354 799600169 560189780 55938794 286711187 352371464 1026112134 285276538 1460183348 887106706 1846531579 1720650208 484803512 31647423 104418702 229678539 728150600 983236569 1400604020 1177082385 1829849018 771612950 1 ans1 ta1 ans2 ta2 prt1 1.0000000 0.0000000 prt1-2-T