In the simplex method, we have occasion to compute the inverse of a matrix for which only one column is different from that of a matrix whose inverse if already known. Suppose that we have a non- singlar matrix B = (b1, b2, . bn) and that B-1 is known. Now we replace column r of B with a and wish to compute the inverse of Ba = (b1, b 2, br-1, a, br+1, . . ., bn). If the columns of B and Ba are viewed as two bases of En, then Ba is obtained from B by changing a single vector in the basis. Use this to derive the inverse of Ba as a function of B-1. B-1 = 204 516 793 where the second column of B is replaced by a random vector in R3 . You may read on elementary transformations, present the theory and write a code to generate the output.

Q: If A is a 3x3 matrix and det(A) = 7, what is det(2A)?

A: Solution :-  Given : A is a 3×3 matrix               And det(A) =7

Q: How do you find the inverse matrix

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Q: If matrix A is 12 xc and matrix K is 4 x t, their product AK is r x 7, what are the values of c, t,…

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Q: ✓ 1.6 Each pair of matrices differ by one row operation. Use this operation to compare det(A) with…

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Q: The 3 × 3 matrix B satisfies the equation B^3 = −B. Show that B cannot have an inverse

A: We proved that, the matrix B cannot have an inverse if it satisfies the equation…

Q: 4. Suppose we have n x n invertible matrices A and B. a. Is the following property true or false?…

A: 4 Given Aand B are the n×n matrices. a We have to check whether the property AB2=A2B2 is true or…

Q: Use the following set of equ 2x1+ X2- X3 = -1 X2+ X3= 2 X1+ 2x2-X3=-1 Using Gauss-Jordan elimination…

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Q: Suppose that B is a square matrix with det(B) = -2. Find each of the following. (a) det(B6) = (b)…

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Q: Find the range of a (2 × 3) matrix B with rank(B) = 2

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Q: Write down the (1,2) minor of the matrix 1 -1 3 -1 1 01 45

A: Given A=1-11-101345

Q: 2 -1 3 1 0 0 1 A = -1 2 no

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Q: Consider the matrix in the image (i) Determine the inverse matrix B^−1 , of B. (ii) Using the…

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Q: 7. Let A₁, A2, A3, A, be 3 x 2023 matrices and suppose A₂ R₁++R 2R₁+R₂, 3R₁ As A₁. (a) Write down a…

A: The elementary row Matrix E is obtained by applying the elementary row operation on the identity…

Q: Write the 4 x 4 elementary matrix which accomplishes the row operation R3 - 5 R2 ---> R3 when you…

A: let  I be the 4×4  identity matrix I=1000010000100001

Q: Write down the (3,3) entry of the inverse of the matrix [1 2 3 122 1 1 1 A

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Q: 2x1 - 2х2 + 4хз (d) 3x1 – 3x2 + 6x3 5х2 + 2хз -3 -4 9

A: Given information: The given system of linear equation is  2x1-2x2+4x3=-33x1-3x2+6x3=-45x2+2x3=9.…

Q: 2. Let A be an (m x n)-matrix and B an (n xt)-matrix over R. (a) Show that row(AB) Crow (B).…

A: Let A be an m×n matrix and B an n×t matrix. To prove that RAB⊆RB Let a1,a2,...,am are the row vector…

Q: If matrix [A] is a 5x5 matrix and a matrix [Z] is obtained by the row operations of replacing Rowl…

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Q: в - C = -2 F = G - E = -1 155 14N o 9, O72 D 54 3. 15 4. O 35 57 206 6, 408

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Q: (ЗАТ + 4CТВ)Т- 54 - 4B

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