You are given the system of equations 2x + 4y = 10 3x + 2y = 7 Which of the following is true about the system above? ? With Cramer's rule, the value of x is $x = \frac{\begin{vmatrix} 10 & 4\\ 7 & 2 \end{vmatrix}}{8}$ ? The system has no solution. ? The determinant of the coefficient matrix is -8 ? With Cramer's rule, the value of y is $y = \frac{\begin{vmatrix} 2 & 10\\ 3 & 7 \end{vmatrix}}{8}$ ? With Cramer's rule, the value of y is $y = \frac{\begin{vmatrix} 2 & 10\\ 3 & 7 \end{vmatrix}}{8}$
Added by Timothy R.
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Now, let's use Cramer's rule to find the value of r: | 10 4 | | r | | 10 | | 7 1 | * | y | = | 7 | By replacing the first column of the coefficient matrix with the constant terms, we get: | 10 4 | | r | | 10 | | 7 1 | * | y | = | 7 | The Show more…
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The determinant of the coefficient matrix is |A| = | -1 2 -3 2 0 1 3 -4 4 | = 10. Since |A| ≠ 0, you know that the system has a unique solution, and Cramer’s Rule can be applied to solve it as follows: x_1 = | 1 2 -3 0 0 1 2 -4 4 | / 10 = 4/5, x_2 = | -1 1 -3 2 0 1 3 2 4 | / 10 = -3/2, x_3 = | -1 2 1 2 0 0 3 -4 2 | / 10 = -8/5. (a) Use Cramer’s Rule to solve the following systems of linear equations, if possible. i. 4x_1 - 2x_2 = 10 3x_1 - 5x_2 = 11 ii. 3x_1 + 3x_2 + 5x_3 = 1 3x_1 + 5x_2 + 9x_3 = 2 5x_1 + 9x_2 + 17x_3 = 4 iii. 2x_1 + 3x_2 + 5x_3 = 4 3x_1 + 5x_2 + 9x_3 = 7 5x_1 + 9x_2 + 17x_3 = 13 (b) ⋆ Explain why Cramer’s Rule works. [Hint: Use the problem 8.]
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Use Cramer's rule to find the solution to the following system of linear equations: 7x + 4y = 3 and Sr + 9y = 1. The determinant of the coefficient matrix is 5.
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Solve each system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. $$\left\{\begin{array}{rr} 2 x-3 y= & -1 \\ 10 x+10 y= & 5 \end{array}\right.$$
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