Please answer all four questions and show work.
Please answer all four questions and show work. Find the inverse of each matrix using the...
1. For each of the following systems of linear equations, find: • the augmented matrix • the coefficient matrix • the reduced row echelon form of the augmented matrix • the rank of the augmented matrix • all solutions to the original system of equations Show your work, and use Gauss-Jordan elimination (row reduction) when finding the reduced row echelon forms. (b) 2 + 2x W 2w - 2y - y + y + 3z = 0 = 1 +...
Use Gaussian elimination to find a row echelon form (not reduced row echelon form) of the augmented matrix for the following system, and then use it to determine for which value of a the following system has infinitely many solutions. x - 2y + 4z = 1 * +3y + z = -9 2x - 3y + az = 0
For the following exercises, solve a system using the inverse of a 3 x 3 matrix. 16.4x + 4y + 4z = 40 4 4 х 140 2x - 3y + 4z = -12 -3 4 y - x + 3y + 4z = 9 -1 3 4 2 -12 2 G
(5 points) The following augmented matrix is in reduced row echelon form. Decode from the matrix the solution of the corresponding system of linear equations (using the variables X1, X2, and x3) or state that the system is inconsistent. (if a free variable is needed use the parameter t.) 1 0 3121 0 1 53 Lo 0 olo) con (10 points) Use row operations to compute the inverse of the matrix A = [ 53 -2] and use it to...
PLEASE ANSWER ALL PARTS 1. (2 points) For the matrix A=| 3 | 6 | Evaluate (a) A, AA* and AA; (b) the value P (A), where P(x)-x3-1. 2. (1 point) Compute the determinant of the matrix A = | α β 2 -8 6 8 2 -7 7 10 3, (1 point) Compute | 1 -3 0 6 4. (1 point) Find the inverse matrix A-' of the matrix A=1 5 3-2 7 4 -3 5. (3 points) Find...
1. Write a MATLAB function that takes a matrix, a row number and a scalar as arguments and multiplies each element of the row of the matrix by the scalar returning the updated matrix. 2. Write a MATLAB function that takes a matrix, two row numbers and a scalar as arguments and returns a matrix with a linear combination of the rows. For example, if the rows passed to the function were i and j and the scalar was m,...
Find the augmented matrix of the linear system X +y+z= -8 X – 3y + 3z = -4 X – Y + 2z = -6. Use Gauss-Jordon elimination to transform the augmented matrix to its reduced row- echelon form. Then find the solution or the solution set of the linear system.
9. Solve. If using rrefon calculator to solve. Write the initial matrix, final matrix, and the solution. 10. Show whether (2,1,0,1) satisfies the system below. The order is (x, y, z, w). x - y + z = -4 2x - 3y + 4z = -15 (5x + y - 2z = 12 x+y+Z+W=4 -x +2y +z = 1 2x + 3y + z-w=6 -2x+y - 22 +2w = -1 11. A truck gets 16 mpg in the city and...
2. Find the augmented matrix of the linear system X – y + z = 7 x + 3y + 3z = 5 X – Y – 2z = 4 Use Gauss-Jordon elimination to transform the augmented matrix to its reduced row- echelon form. Then find the solution or the solution set of the linear system.
1o. Solve by using a Matrix Inverse x+3y+22 3 11. Graph the solution set of the given system of inequalities. 2x +3y 2 12 7x +4y 2 28 rs8 ys9 2 Find the surm ofSf(x,JAr, with x1-0, x,-2, x,-4. x.-6,and ?-05 Write the first five terms of the arithmetic sequence. ,16 and ao 46 nonument is constructed by laying a row of 150 bricks at ground lev ks, is entered on that; a third row, with five fewer bricks, is...