A-1121 1 11353 4 5(a) Calculate det(A). Hint: consider performing some elementary row operations.(b) Is A an invertible matrix? Justify your answer.(c) Denote by V₁, V2, V3, V4 the columns of A, considered as vectors in R4.(i) Are vectors V₁, V2, V3 linearly independent? Justify your answer.(ii) Do vectors V1, V2, V3 span R4? Justify your answer.(iii) Do vectors V₁, V2, V3, V4 span R4? Justify your answer.

Given the matrix .(a) We will find the determinant using the elementary row operations.The product…

Answered: A = 1 3 1 135 2 345 Calculate det(A).…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let A be a 3x3 matrix such that Assume that the vector V = E -2 is a solution of the matrix equation 3 Enter the vector V₁ in the form [C₁, C2, C3]: -12 12 -24 Find three vectors V₁, V₂, V3, different from V, which are also solutions of this equation. Enter the vector V₂ in the form [C1, C2, C3]: Nul (A) = Span (3) ED Enter the vector V3 in the form [C1, C2, C3]: Ax=
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Make LU Factorization. b. 2 -4 4 -2 6 -9 7 -3 -4 Determine the column vectors of (b) are linearly independent or not by using the information obtained after making LU factorization. +78
Let v1, V2 and v3 be three linearly independent vectors in R3. (a) Find the rank of the matrix A = [(v1 – v2) (v2 – v3) (V3 – V1)]. (b) Find the rank of the matrix B = [(v1 + v2) (V2 + V3) (V3 + V1)].
а +с] a) Let S Find three vectors in R3 so that each vector a - b - a in S can be written as a linear combination of the three vectors. Are these vectors linearly independent? Justify your answer. 1 -2 1 1 1 -1 Let A = 2 Determine whether the rows of A are 4 4 -5 [-2 -4 4 -1 linearly independent. Evaluate | – 2A²| and13A¬1|.
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