9.12 Use Gauss-Jordan elimination to solve: 2x1 + x2x3 =1 5x1 + 2x2 + 2x3 =...

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9.12 Use Gauss-Jordan elimination to solve: 2x1 + x2x3 =1 5x1 + 2x2 + 2x3 = -4 3x1 + x2 + x3 = 5 Do not employ pivoting. Check your answers by substituting them into the original equations. 10.3 (a) Solve the following system of equations by LU decomposition without pivoting X₁ +7x2 - 4x3 = -51 4x14x2 +9x3 = 62 12x1x2 + 3x3 = 8 (b) Determine the matrix inverse. Check your results by verifying that [A][A]¹[1]. 17.12 An investigator has reported the data tabulated below for an experiment to determine the growth rate of bacteria k (per d), as a function of oxygen concentration c (mg/L). It is known that such data can be modeled by the following equation: с k= kmaxe Cs+2²2² where c, and Kmax are parameters. Use a transformation to linearize this equation. Then use linear regression to estimate c, and Kmax and predict the growth rate at c = 2 mg/L. 0.5 1.1 0.8 1.5 2.4 5.3 2.5 7.6 4 8.9 9.12 Use Gauss-Jordan elimination to solve: 2x1 + x2x3 =1 5x1 + 2x2 + 2x3 = -4 3x1 + x2 + x3 = 5 Do not employ pivoting. Check your answers by substituting them into the original equations. 10.3 (a) Solve the following system of equations by LU decomposition without pivoting X₁ +7x2 - 4x3 = -51 4x14x2 +9x3 = 62 12x1x2 + 3x3 = 8 (b) Determine the matrix inverse. Check your results by verifying that [A][A]¹[1]. 17.12 An investigator has reported the data tabulated below for an experiment to determine the growth rate of bacteria k (per d), as a function of oxygen concentration c (mg/L). It is known that such data can be modeled by the following equation: с k= kmaxe Cs+2²2² where c, and Kmax are parameters. Use a transformation to linearize this equation. Then use linear regression to estimate c, and Kmax and predict the growth rate at c = 2 mg/L. 0.5 1.1 0.8 1.5 2.4 5.3 2.5 7.6 4 8.9

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