RREF[A decode it to equations, and solve the homogeneous system of linear equations corresponding to the coefficient matrix A below. 6 -2 0 A = - 6 -5 0 20

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.2: Norms And Distance Functions
Problem 49EQ
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1 2 12]
1. Find RREF(A], decode it to equations, and solve the homogeneous system
of linear equations corresponding to the coefficient matrix A below.
6 -2 01
- 6 -5 0
2 0
A =
2. Solve the system having augmented matrix (A|b] below by finding A
and calculating x = A b.
-1 10
0 -1 1
[A|b]
3
3. (a) Use Kirchhoff's laws of electrical circuits to write a
system of 3 linear equations in 3 unknowns (current flows I1-I3) for
the junctions 1 and 2 and loop 1 indicated in the circuit
below with resistances R, R2, and R, given as 3, 1, and 2 ohms,
respectively, when a potential of V-12 volts is applied.
(b) Give the solution.
4. Find the least squares regression line for the points
(2, 1), (3, 1), and (5, 2). Remember to include error analysis.
5. Prove that (A)-- (A-1)7 for all nxn invertible matrices A.
Transcribed Image Text:1 2 12] 1. Find RREF(A], decode it to equations, and solve the homogeneous system of linear equations corresponding to the coefficient matrix A below. 6 -2 01 - 6 -5 0 2 0 A = 2. Solve the system having augmented matrix (A|b] below by finding A and calculating x = A b. -1 10 0 -1 1 [A|b] 3 3. (a) Use Kirchhoff's laws of electrical circuits to write a system of 3 linear equations in 3 unknowns (current flows I1-I3) for the junctions 1 and 2 and loop 1 indicated in the circuit below with resistances R, R2, and R, given as 3, 1, and 2 ohms, respectively, when a potential of V-12 volts is applied. (b) Give the solution. 4. Find the least squares regression line for the points (2, 1), (3, 1), and (5, 2). Remember to include error analysis. 5. Prove that (A)-- (A-1)7 for all nxn invertible matrices A.
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