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(1 point) Assume that A is a matrix with three rows. Find the elementary matrix E...
(1 point) Suppose that A is a 3 × 3 matrix. For each of the question a A after the given row operation is performed. Then give E-1 d), find the elementary matrix E such that EA gives the matrix resulting from
Write down the elementary matrix E that when multiplied on the left of a 5 × 5 matrix, performs the row operation R2 → R2 + –3R1.
Algebra of matrices. 3. (a) If A is a square matrix, what does it mean to say that B is an inverse of A (b) Define AT. Give a proof that if A has an inverse, then so does AT. (c) Let A be a 3 x 3 matrix that can be transformed into the identity matrix by perform ing the following three row operations in the given order: R2 x 3, Ri R3, R3+2R1 (i) Write down the elementary...
4. For the given elementary row operation e, find its inverse operation e-1 and the elementary matrices associated with e and e-1, e = R 2 R, the e: Add - 2 times the second row to the third row of 3 x 3 matrices.
(1 point) Consider the matrix 7 -8 0 -8 -5 -1 -8 8 -4 (a) On the matrix above, perform the row operation 6R3 + R2 -> R2. The new matrix is: (b) On the original matrix, perform the row operation -17R2 -+ R2. The new matrix is: (c) On the original matrix, perform the row operation R2 R3. The new matrix is:
(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) Consider the matrix -5 7 8-9 20 -30 8-3 -15 -19 9 -4 10-11 5-8 (a) On the matrix above, perform the row operation R1 15 R1 . The new matrix is: (b) Using the matrix obtained in your answer for part (a) as the initial matrix, next perform the row operations () R3 R3 15R1, (iii) R4→R4+10R1. The new matrix is: (c) Using the matrix obtained in your answer for part (b) as the initial matrix, next...
(1 point) Suppose that 1 1 -2 5 5 2 145 Given the following descriptions, determine the following elementary matrices and their inverses. matrix Ezi subtracts 5 times the first row of A from the second row of A E21 = The elementary matrix Ez1 subtracts -6 times the irst row of A from the second row of A The permutation matrix Piz switches the first and second rows of A P12 The elementary matrix Ezi subtracts 7 times the...
(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...
(6) Given the augmented matrix 112 -5 -1 10 1 which of the following row operations would give you the resulting matrix 11 0 lo 2 1 0 -5 -2 - 1 1 - 1 - 1 ? (a) -3R2 - R3 - R (b) 3R2 + R3 R3 (C) -3R2 + R3 R3 (d) R3 - 3R2 + R2 (e) none of the above (7) Find a point where the tangent line to the curve (x)-(x-2)(x2-x-11) is horizontal (a)...