Using a computer with four significant digits with chopping, the Gaussian elimination with partial pivoting solution to the following system: 0.0030x1 + 55.23x2 = 58.12 6.239x1 - 7.123x2 = 47.23 Is: (A) x1 = 26.66; x2 = 1.051 (B) x1 = 8.769; x2 = 1.051 (C) x1 = 8.800; x2 = 1.000 (D) x1 = 8.771; x2 = 1.052 NOTE: Show how you derive the answer using Gaussian elimination and highlight any pivoting that you do.
Added by Elisa P.
Close
Step 1
The original equation is: \[ 0.0030x + 55.23x^2 + 58.12 - 6.239x - 7.123x^2 = 47.23 \] Combine like terms: \[ (55.23x^2 - 7.123x^2) + (0.0030x - 6.239x) + 58.12 = 47.23 \] \[ 48.107x^2 - 6.236x + 58.12 = 47.23 \] Show moreā¦
Show all steps
Your feedback will help us improve your experience
Krishna G and 64 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Using Gaussian elimination with backward substitution and two-digit rounding arithmetic, the solution of the following system is: 4x1 - x2 + x3 = 8 2x1 + 5x2 + 2x3 = 3 x1 + 2x2 + 4x3 = 11 a. x1 = 1.0, x2 = 0.98, x3 = 2.9 b. x1 = 1.0, x2 = -0.98, x3 = -2.9 c. x1 = 1.0, x2 = -0.98, x3 = 2.9 d. x1 = 1.1, x2 = -0.98, x3 = 2.9
Madhur L.
Reduce to $U x=c$ (Gaussian elimination) and then $R x=d:$ $$ A x=\left[\begin{array}{llll} 1 & 0 & 2 & 3 \\ 1 & 3 & 2 & 0 \\ 2 & 0 & 4 & 9 \end{array}\right]\left[\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{array}\right]=\left[\begin{array}{r} 2 \\ 5 \\ 10 \end{array}\right]=b $$ Find a particular solution $x_{p}$ and all nullspace solutions $x_{n}$.
Vector Spaces
Solving $A x=0$ and $A x=b$
(a) Express the system in the matrix form $A X=B .$ (b) Approximate $A^{-1}$, using four-decimal-place accuracy for its elements. (c) Use $X=A^{-1} B$ to approximate the solution of the system to four-decimal-place accuracy. $$\left\{\begin{array}{l} 1.9 x-3.2 y=5.7 \\ 2.6 x+0.4 y=3.8 \end{array}\right.$$
Systems of Equations and Inequatities
The Inverse of a Matrix
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD