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3. Let A 2 -30 1 0 -2 2 0 (i) Compute the determinant of A using the cofactor expansion technique along (a) row 1 and (b) column 3. (ii) In trying to find the inverse of A, applying four elementary row operations reduces the aug- mented matrix [A1] to -2 0 0 0 0 -2 2 1 3 0 1 0 1 0 -2 Continue with row reductions to obtain the augmented matrix [1|A-') and thus give the in-...
2,3, 6, 7 1. Without matrices, solve the following system using the Gaussian elimination method + 1 + HP 6x - Sy- -2 2. Consider the following linear system of equation 3x 2 Sy- (a) Write the augmented matrix for this linear system (b) Use row operations to transform the augmented matrix into row.echelon form (label all steps) (c) Use back substitution to solve the linear system. (find x and y) x + 2y 2x = 5 3. Consider the...
FEL 1120 Linear Systems 2016 PART NO. 1. SOLVE THE FOLLOWING PROBLEMS Problem No. Solve the following system of linear equations using elementary row operations (do not use matrices when solving it) Show every step when modifying the system to REF 2. Show REF of your system 3. Show all steps to modify the system to 4. Show RREF of your system 5. Write the solution ( y-2v + x + 3y + 2z = 1 -V + 2x +...
Solve the system using an augmented matrix and elementary row operations. x-4y+62=-3 3) -x +5y – 2z = -1 2x+y-z=7
(6 points) Evaluate the following system using the augmented matrix method. When performing row reduction, be sure to indicate your row operations. x 2x -x + 2y + 5y + 4y – + – 2= z = 2z = -3 1 3 (12 points) Evaluate the following system using Gauss-Jordan elimination. When per- forming row reduction, be sure to indicate your row operations. 2x x -x (a) – + + y + z = y + 2z = 3y +...
and 11 -5 -5] -1 1 0 are inverses of each other to solve the following system of -1 0 1 11 55 Use the fact that the matrices 1 6 5 [ 1 5 6 linear equations. X + 5y + 5z = 38 X + 6y + 5z = 44 x + 5y + z = 38 , y = , and z= The solution is x = (Type integers or simplified fractions.)
2 +2y - 2=3, I-y=2, 2.0 + y - 2= 5. 1. Write the system as an augmented matrix and perform some elementary row operations to make it in row reduced row echelon form. 2. What is the rank of the augmented matrix? How many free variables does this system have. 3. Write the solutions of the system in parametric form. 4. Consider the following system 2 + 2y - 2=3, r-y=2, 2.x + y -2=1. (The only difference is...
O 2 1 1 02 O -2 102 5. Let A 0 -2 0 B 0 and C O 1 0 4 1. 1 0 4 -1 0 4 (a) Find an elementary row operation that transforms A into B. O 2 (b) Find an elementary row operation that transforms B into C. (c) By means of several additional operations, transform C into I3 (d) What is the rank of the matrix A? Explain.
Let -1 1 0 A= 1 1 0 0 -1 1 -1 1 1 21 22 = 24 1 b= ta 19 2 3 Then Az = b represents the following system: 21 - 22 +23 = 1 21-23 + 14 = 2 -22 + 23 - 24 = 3. Select one: 0 True O False Check 2 + 2y = 1 After performing two elementary operations starting with the system one obtains the system 3y = a 2 +...
29&30 please 3 -23 4 3-2 25. 3 4926. |0 1 1 0 0-2 1 2-5 Finding a Basis In Exercises 27-30, find a basis B for the domain of T such that the matrix for T relative to B is diagonal. 27. T: R2→R-T(x, y) = (x + y, x + y) 28. T: R3→R, Tu, y, z) (-2x +2y -3z, 2r y -6z. 2y) a + (af+ 2b)s 29. T: Pi-Pi T(a + bx) 30. T: P㈠Pg Tle...