In determinants, cofactor is given by :
Cij = (-1)i+j * Mij where, C ij = cofactor and (-1)i+j is the sign associated with the minor M ij .
So, sign for :
C13 = (-1)1+3 = (-1)4 = +1
C23 = (-1)2+3 = (-1)5 = -1
C33 = (-1)3+3 = (-1)6 = +1
C41 = (-1)4+1 = (-1)5 = -1
C34 = (-1)3+4 = (-1)7 = -1
2. Determine the signs to be attached to the relevant minors in order to get the...
2. Determine the signs to be attached to the relevant minors in order to get the following cofactors of a determinant: C131, IC231, IC33l, C411, and 1C341.
2. Determine the signs to be attached to the relevant minors in order to get the following cofactors of a determinant: 1613, C231, IC33, C411, and 1C34. 1 4. Test whether the following matrices are nonsingular: 4 0 7 -1 0 19 1 - 3 (0) 1 1 4 7 1 0 13 -3 -4 4 -21 -4 9 5 -S 6 0 (d) 3 0 1 7 0 3 10 8 6 II ob 12
3 6 9 04 7 9-18 2. Determine the signs to be attached to the relevant minors in order to get the following cofactors of a determinant: C131, C231, 1C33, C411, and 1C341.
EXERCISE 5.2 1. Evaluate the following determinants: 2. Determine the signs to be attached to the relevant minors in order to get the following cofactors of a determinant: (C13l, IC23i, (C3sl. Canl, and Cu). 6. Find the minors and cofactors of the third row, given EXERCISE 5.3 4. Test whether the following matrices are nonsingular: EXERCISE 5.4 4. Find the inverse of each of the following matrices: 6. Solve the system Ax=d by matrix inversion, where EXERCISE 5.5 1. Use Cramer's rule to solve the following equation systems: 3. Use Cramer's...
2 Find the minors and cofactors of third row 9 11 41 nr nd W 6 10 4
6. Find the minors and cofactors of the third row, given 9 11 4 A= 3 27 6 10 4 4. Find the inverse of each of the following matrices: 4 -2 1 100 (a) E = 7 3 0 (CG= 0 0 1 2 0 1 0 1 0 -1 2 100 (6) F= 03 (d) H= 0 1 0 4 02 0 0 1 1
linear algebra class due in 30minutes please help ASAP! Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example shows the statement is not true in all cases or cite an appropriate statement from the text. (a) To find the determinant of a triangular matrix, add the entries on the main diagonal false, the determinant of a triangular...
LarPCalc8 8.1.012 45 points 1. Determine the order of the matrix. 47 15 0 -1 0 3 3 6 7 -3 1 O-15 points LarPCalc8 8.1.020. 2. Write the augmented matrix for the system of linear equations. {Sx 4y-2z 24 -21y +8z -3 8x + O-15 points LarPCalc8 8.1.022 My Nete 3. Write the system of linear equations represented by the augmented matrix. (Use the variables x, y, z, and w, if applicable.) 7 -5-4 3 39 8 O-5 points...
QUESTION 2 (a) Consider the attached character table for the point group, D3d. (i) Determine the order of the point group. Show all work. (ii) Determine the order of the point group using any other method. rave? (iii) Which irreducible representations are orthogonal? Show all work. (iv) Give the completely symmetric irreducible representation.
2. Write the product of a sequence of elementary matrices which equals the given non-singular matrix: [ 11 2 3 3. Given the matrix A = 01 - write the matrix of minors of A, the matrix of cofactors of A, the adjoint 12 2 2 matrix of A, and use the adjoint of A, to write the inverse of A. 4. Determine whether the set of vectors is linearly dependent or linearly independent. Justify your answer. 13