4. Calculate the following determinants, using the row reduction techniques from class. (a) det31 1 (b)...
a)Use row reduction and/or cofactor expansion to calculate the
determinant of
c) Calculate the following determinants, using your answer to
part a
det(A^−1 ) det(2A) det(A^2 ) det(A^T A)
3 3 3 -1 2 2 A= 1 9 6 2 2 2 4 2
B: Calculate the determinant of the following matrix by using row reduction to produce an upper triangular form: 2 marks 10 4 21 B=0 -4 3 -5 -1 -12
The technique is called Cofactor expansion and row reduction
Use the techniques from 2.1 and 2.2 to calculate the following determi- nant 4 0 8 10 2 1 0 2 3 0 3 3 4 4 4 0 0 3 1 -2 -1 0 -7 4 4
please provide detailed and clear solutions for the
following
2-6 3 2- 0 -103-5 Calculate the determinants of A and B -1 4 (use either appropriate row and coumn expansions or elementary row operations and the properties of determinants). Are A and B invertible? Calculate their inverses if they exist 1b. Are the columns of A linearly dependent or linearly independent? Find the dimension of Nul A and the rank of A. What can you say about the number of...
Answer these explanations:
ADDING A MULTIPLE OF THE ith ROW TO THE jth row. 5.4 Example 6: Create a 5 by 5 matrix, E by typing: Type: ΕΞ11 2-134:10-1-2-1; 8 3 2 11:10-2-3-2:1112-1]. Find det(E) by typing: Type DE det(E) Note: Adding a multiple of ith row of E to the jth row in MATLAB can be done as follow. Values of i, j and k must be defined (entered) first. In the following line we choose i = 3,J...
(1 point) Perform one step of row reduction, in order to calculate the values for x and y by back substitution. Then calculate the values for x and y. Also calculate the determinant of the original matrix. (Note: since the determinant is unchanged by type 3 row operations, it will be easier to calculate the determinant of the row reduced matrix.) (12 32] [31 = [1] det =
Use row-reduction to put the following matrix to reduced row echelon form. 1 5 4 2 1 2 0 0 3 0 Show each step.
i need simple answers ( not over detailed) thanks
Q.7) Evaluate the given determinants by using row reduction. 14 -9921 - 2 5 6 4 1 2 -5 -3 1 -2 0 -21 1o o 0 0 0 0 0 2 b) 5 0 o 0 -1 0 0-3 - 4 0 0 0 0 0 0 0 15 000 0 10 000 - 4 O 0300 0 0 0 1 0 JO-2000 0
(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 +...
Determinants and linear transformations 4. (a) Let A be the matrix 1 -2 4 1 3 2 11 i) Calculate the determinant of A using cofactor expansion of row 3. (ii) Is A invertible? If so, give the third column of A1 (you do not have to simplify any fractions) (b) Let B be the matrix 0 0 4 0 2 8 0 4 2 1 0 0 0 7 Use row operations to find the determinant of B. Make...