1. Let x E C" and y E C™, with y # 0. Consider the m x n matrix defined by A = yx*. (a) Show that rank A = 1. (b) Show that ||A||2 = ||x||2||y||2- (c) Show that ||A||F = ||x||2||y||2 (which is the same as ||x||F||y||F).

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A: Given: 02-135-2-3-51X=-1000-50004 If AX=B, then X= A-1B. We know that A-1=adjAA and adjA= cofaijT

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A: I am attaching image so that you understand each and every step.

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A: Particular solution of the system  X' = AX + b is: XP=Φ∫Φ−1b dt here Φ is fundamental matrix.

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A: A matrix A is said to be singular if its determinant is zero .

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Q: e singular values

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Q: For a non-singular matrix A, A^(-1) is equal to: (adj(A)) / det(A) det(A) x (adj(A)) det(A) x A

A: Explained below

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.