2. Let 0 1 -1 2 1 0 1 -1 2 --()-) 1 1 5 0 -2 1 A = 2 1 5 1 0 1 1 2 В 1 0 6 1 9 -3 8 (a) Show that A and B are not row-equivalent. (b) Compute the values of rank(A) and rank(B). (c) Compute the general solution for each of the SLES Ax=0 and Bx = 0. (d) Find a solution of the SLE Bx = 0 that is not contained in the solution set of Ax = 0. (e) Is the SLE Ax = b consistent for every b e R³? Is the SLE Bx = b consistent for every beR? In the affirmative case, justify your answer. In the negative case, find a vector BER³ such that the SLE is inconsistent.

Q: a) Identify the basic variables. b) What is the value of x1? c) What is the value of x2? d) What is…

A: Since there are two equations, so atleast two 0 must present in the last row,  Here only two 0 zero…

Q: Let A be an m × n matrix (a) Show that dim Row A + dim Nul A =n (b) Show that dim Col A + dim Nul A"…

A: I don't have idea about part (c). Let's Solve part (a) and part(b),

Q: 5. Diagonalize A (if possible), that is, find a representation of the form A = PDP-¹, where D is…

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Q: 10. Suppose that A is an n x n matrix with real entries such that the diagonal elements are all…

A: The problems with proof can be solved by using the concepts in linear algebra. A diagonally dominant…

Q: 8. Let A be the 10 x n matrix formed by the first n columns of the 10 x 10 Hilbert matrix. Let c be…

A:

Q: Suppose that AB C, where A is 3x4 and C is 3x2. Then B must be 4 To find the entry c21 of C = AB,…

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Q: Compute the Cholesky decomposition of the matrix 41 40 40 41 Show all the details. A =

A:

Q: 10. Show that if M₁ = (1 8), M₂ = (89) (15). then the span of {M₁, M2, M3} is the set of all…

A:

Q: 3. Suppose A € M5,5 (R) and det(A) = -3. Find each of the following: (a) det(A¹), det (A-¹),…

A: Given  matrix   A∈M5x5  and  det (A) = -3  i.e.    A = -3 (.)  If  any two rows ( columns ) of a…

Q: 4. Find the null space and column space of the matrices 0 1 1 -2 1 1 0 1 22-4 0 -1 0 1 -3 A = 1 2 3…

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Q: Consider the system Ax = b where A = [11] and b= [¹₂] A basis for the null space of A is given by…

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Q: Given the set of matrices M = {I, A, B, C, D, K} where 1 -( :) 0 I = 0 1 --(: :) C = -1 1 +-(13) :)…

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Q: 1 1 1 2 1 X1 1 X2 1 X3 A = 1 3 Y1 b = Y2 Уз. 14 * - [:] a X =

A:

Q: For given data (xi,yi), i = 1, 2..., n, the solution of equations a ac Σlyi - (cx; + d)]² = 0 i=1 od…

A: Look inside the summation its like summing up square of distances of y to some fixed cx+d.Least…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.