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| public:calculator:guides:dm32_simultaneos_equations [17/04/26 18:20 BST] – john | public:calculator:guides:dm32_simultaneos_equations [19/04/26 21:07 BST] (current) – [Further Information] john | ||
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| These equations can be represented in matrix form | These equations can be represented in matrix form | ||
| - | | A D G | | x | | J | | + | '' |
| - | | B E H | | y | | + | | A D G | | x | |
| + | | B E H | | y | = | K | | ||
| + | | C F I | | z | | L | | ||
| + | '' | ||
| + | This is effectively | ||
| - | ===== Further Information ===== | + | '' |
| + | and therefore | ||
| + | |||
| + | '' | ||
| + | |||
| + | or | ||
| + | |||
| + | '' | ||
| + | |||
| + | The unknown matrix is obtained by multiplying '' | ||
| + | |||
| + | They are entered sequentially in the order | ||
| + | |||
| + | '' | ||
| + | |||
| + | ===== Use ===== | ||
| + | |||
| + | Enter the values of the 3x3 matrix and the 3x1 column vector by using prog. A | ||
| + | |||
| + | * < | ||
| + | * Enter each value at the prompt followed by < | ||
| + | * Once all values '' | ||
| + | * find the determinant of the coefficient matrix with prog '' | ||
| + | * this is not required for a simple solution, but might be useful for other purposes? | ||
| + | * **I**nvert the coefficient matrix A with prog. '' | ||
| + | * < | ||
| + | * **M**ultiply the column vector by this inverse matrix using prog. '' | ||
| + | * < | ||
| + | * This gives the resulting '' | ||
| + | |||
| + | ===== Examples ===== | ||
| + | |||
| + | ==== 3 x 3 ==== | ||
| + | |||
| + | A system of equations with 3 unknowns '' | ||
| + | |||
| + | |||
| + | '' | ||
| + | |||
| + | '' | ||
| + | |||
| + | '' | ||
| + | |||
| + | <note warning> | ||
| + | |||
| + | Beware! | ||
| + | |||
| + | You enter each value in sequence going **down the columns** in sequence | ||
| + | |||
| + | Which is the opposite sense to the way matrices are entered in DM15L and DM41X | ||
| + | |||
| + | </ | ||
| + | |||
| + | * < | ||
| + | * 23 < | ||
| + | * 8 < | ||
| + | * 4 < | ||
| + | * 15 < | ||
| + | * 11 < | ||
| + | * 15 < | ||
| + | * 17 < | ||
| + | * 6 < | ||
| + | * 12 < | ||
| + | * 31 < | ||
| + | * 17 < | ||
| + | * 14 < | ||
| + | * Find the inverse < | ||
| + | * Multiply < | ||
| + | * Display shows solutions | ||
| + | * '' | ||
| + | * '' | ||
| + | * '' | ||
| + | * You can inspect the inverted matrix by running '' | ||
| + | * < | ||
| + | * '' | ||
| + | * '' | ||
| + | * etc....etc... | ||
| + | * You can re-invert A back to the original state by running prog '' | ||
| + | * You can see the determinant of A by running prog '' | ||
| + | |||
| + | ==== 2x2 ==== | ||
| + | |||
| + | The programs expect a 3x3 matrix. If the system is 2x2 you have to use dummy values to pad out to 3x3 | ||
| + | |||
| + | Set '' | ||
| + | |||
| + | e.g. | ||
| + | |||
| + | '' | ||
| + | |||
| + | '' | ||
| + | |||
| + | This becomes | ||
| + | |||
| + | '' | ||
| + | |||
| + | '' | ||
| + | |||
| + | '' | ||
| + | |||
| + | and is entered | ||
| + | |||
| + | * < | ||
| + | * 2 < | ||
| + | * 8 < | ||
| + | * 0 < | ||
| + | * 3 < | ||
| + | * 4 < | ||
| + | * 0 < | ||
| + | * 0 < | ||
| + | * 0 < | ||
| + | * 1 < | ||
| + | * 6 < | ||
| + | * 9 < | ||
| + | * 0 < | ||
| + | * Find the inverse < | ||
| + | * Multiply < | ||
| + | * '' | ||
| + | * '' | ||
| + | * '' | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | ===== Further Information ===== | ||
| - | {{tag>}} | ||
| Page created | Page created | ||
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| Page updated : ~~LASTMOD~~ | Page updated : ~~LASTMOD~~ | ||
| + | |||
| + | |||
| + | {{tag> | ||
