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(1 point) Suppose that 1 1 -2 5 5 2 145 Given the following descriptions, determine...
Suppose that and B 4 -2 4 4 -2 2 Given the following descriptions, determine the...
Suppose that and B 4 -2 4 4 -2 2 Given the following descriptions, determine the following elementary matrices and their inverses. a) The elementary matrix E subtracts 5 times the first row of A from the second row of A. Ei- b) The elementary matrix E21 subtracts -3 times the first row of A from the second row of A. Ei- c) The permutation matrix P12 switches the first and second rows of A. 12 d) The elementary matrix...
(1 point) Suppose that: -15 A= and B = 3 -2 -4 -1 5 e) The...
(1 point) Suppose that: -15 A= and B = 3 -2 -4 -1 5 e) The elementary matrix E2.1 subtracts 6 times the first row of B from the second row of B. E2,1 = , Ez1 = f) The elementary matrix E3.1 subtracts -5 times the first row of B from the third row of B. E3.1 = g) The permutation matrix P13 switches the first and third rows of B. P13= ,P3! = h) The elementary matrix E32...
Suppose that: A =[-4 2 -3 3] and B = [-5 -1 5 5 -1 4 -2 -2 -1] Given the following descriptions, determine the following elementary matrices and their inverses. {View Image}
a. The elementary matrix ?1E1 multiplies the first row of A by 1/6.b. The elementary matrix ?2E2 multiplies the second row of A by -4.c. The elementary matrix ?3E3 switches the first and second rows of A.d. The elementary matrix ?4E4 adds 6 times the first row of A to the second row of A.e. The elementary matrix ?5E5 multiplies the second row of B by 1/3.f. The elementary matrix ?6E6 multiplies the third row of B by -4.g. The elementary matrix ?7E7 switches the first and third rows of B.h. The elementary matrix ?8E8 adds...
(1 point) Suppose that: -4 -2 -1 -3 -3 A= 1 and B = -1 -3...
(1 point) Suppose that: -4 -2 -1 -3 -3 A= 1 and B = -1 -3 -1 -4 4 4 -3 -5 Given the following descriptions, determine the following elementary matrices and their inverses. e. The elementary matrix Es multiplies the second row of B by 1/2 Es = f. The elementary matrix Es multiplies the third row of B by -6. Eg = g. The elementary matrix E, switches the first and third rows of B. ,E,= h. The...
3. Let A 2 -30 1 0 -2 2 0 (i) Compute the determinant of A...
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-...
Problem 1 Write your code in the file MatrixOps.java. . Consider the following definitions from matrix...
Problem 1 Write your code in the file MatrixOps.java. . Consider the following definitions from matrix algebra: A vector is a one-dimensional set of numbers, such as [42 9 20]. The dot product of two equal-length vectors A and B is computed by multiplying the first entry of A by the first entry of B, the second entry of A by the second entry of B, etc., and then summing these products. For example, the dot product of [42 9...
Question 1 a. Define the following matrices in a script file (M-file), ? = ( 8...
Question 1 a. Define the following matrices in a script file (M-file), ? = ( 8 9 10 11; 23 9 16 15 ;11 12 3 6; 1 2 8 9 ) ? = ( 2 21 7 15; 12 4 8 22; 23 9 5 13; 23 4 21 22) ℎ = (4 9 12 15) b. Add suitable lines of codes to the M-file to do the following. Each of the following points should be coded in only...
Due in 2 hr (a) Use Octave as a Calculator to answer this question Suppose that A and B are two 8 × 9 matrices. The (i, j)-entry of the matrix B is given by i *j -1. The (i,j)-entry of the mat...
Due in 2 hr
(a) Use Octave as a Calculator to answer this question Suppose that A and B are two 8 × 9 matrices. The (i, j)-entry of the matrix B is given by i *j -1. The (i,j)-entry of the matrix A equals 0 if i +j is divisible by 5 and equals the (i,j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices A and B? Is vector u =[964,-71,4249, 59, 234,-196.97]...
(3 points) Let A be a 4 x 4 matrix with det(A) = 8. 1. If...
(3 points) Let A be a 4 x 4 matrix with det(A) = 8. 1. If the matrix B is obtained from mes the second row to the first, then det(B) = 2. If the matrix C is obtained from A by swapping the first and second rows , then det(C) = 3. If the matrix D is obtained from A by multiplying the first row by 5, then det(D) =
4) a) For the system of equations given, partially row reduce the coefficient matrix in the...
4) a) For the system of equations given, partially row reduce the coefficient matrix in the following careful way: *1 + 2y, - 2 = 5 4x1 +9y1 - 32 = 8 (5x + 12y - 321 = 1 Stage 1: just reduce the matrix first to an upper triangular form U and leave pivot entries as they are (don't multiple to change them to 1's). Reduce from left to right through the columns and from the pivot entry down...
Suppose that and B 4 -2 4 4 -2 2 Given the following descriptions, determine the following elementary matrices and their inverses. a) The elementary matrix E subtracts 5 times the first row of A from the second row of A. Ei- b) The elementary matrix E21 subtracts -3 times the first row of A from the second row of A. Ei- c) The permutation matrix P12 switches the first and second rows of A. 12 d) The elementary matrix...
(1 point) Suppose that: -15 A= and B = 3 -2 -4 -1 5 e) The elementary matrix E2.1 subtracts 6 times the first row of B from the second row of B. E2,1 = , Ez1 = f) The elementary matrix E3.1 subtracts -5 times the first row of B from the third row of B. E3.1 = g) The permutation matrix P13 switches the first and third rows of B. P13= ,P3! = h) The elementary matrix E32...
(1 point) Suppose that: -4 -2 -1 -3 -3 A= 1 and B = -1 -3 -1 -4 4 4 -3 -5 Given the following descriptions, determine the following elementary matrices and their inverses. e. The elementary matrix Es multiplies the second row of B by 1/2 Es = f. The elementary matrix Es multiplies the third row of B by -6. Eg = g. The elementary matrix E, switches the first and third rows of B. ,E,= h. The...
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-...
Due in 2 hr
(a) Use Octave as a Calculator to answer this question Suppose that A and B are two 8 × 9 matrices. The (i, j)-entry of the matrix B is given by i *j -1. The (i,j)-entry of the matrix A equals 0 if i +j is divisible by 5 and equals the (i,j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices A and B? Is vector u =[964,-71,4249, 59, 234,-196.97]...
(3 points) Let A be a 4 x 4 matrix with det(A) = 8. 1. If the matrix B is obtained from mes the second row to the first, then det(B) = 2. If the matrix C is obtained from A by swapping the first and second rows , then det(C) = 3. If the matrix D is obtained from A by multiplying the first row by 5, then det(D) =
4) a) For the system of equations given, partially row reduce the coefficient matrix in the following careful way: *1 + 2y, - 2 = 5 4x1 +9y1 - 32 = 8 (5x + 12y - 321 = 1 Stage 1: just reduce the matrix first to an upper triangular form U and leave pivot entries as they are (don't multiple to change them to 1's). Reduce from left to right through the columns and from the pivot entry down...
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