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Tag: MFDS

Prove Linear Transformation And Find the Nullity

Posted 2 years ago by Ehan Ghalib

Question Let be defined by then, 1. Show that T is a linear transformation 2. What are the conditions on a, b, c such that (a, b, c) is in

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Linear Algebra, Mathematics for Data Science, Solution Repository Linear Transformation, Mathematics for Data Science, MFDS, Nullity, Nullspace, Vector Algebra Leave a comment

Solve the Car Dealer Problem with Generating Functions

Posted 3 years ago by Ehan Ghalib

Question A gasoline car dealer is stopping operations in a city as part of reallocation of company resources to electric cars. It has eight identical sedan cars left in its

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Generating Functions, Mathematics for Data Science, Solution Repository Generating Functions, Mathematics for Data Science, MFDS Leave a comment

Brute Force Approach with Pigeonhole Principle

Posted 3 years ago by Ehan Ghalib

Question A computer program is randomly fed three-digit numbers between 000 and 999 and executes the command immediately after it has been fed 4 three-digit numbers with same sum of

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Counting Principles, Mathematics for Data Science, Solution Repository Counting Principles, Mathematics for Data Science, MFDS, Pigeonhole Principle Leave a comment

Counting Results in a Competition With Ties

Posted 3 years ago by Ehan Ghalib

Question In National Games Championship, a high jump competition is being conducted along with other athletic events. Only n out of m athletes were able to meet the eligibility criteria

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Counting Principles, Mathematics for Data Science, Solution Repository Counting Principles, Data Science, Fubini Numbers, MFDS, Ordered Bell Numbers Leave a comment

Time Taken to Find Rank of a Matrix Using Determinants

Posted 3 years ago by Ehan Ghalib

Question Let be a given matrix with . If the time taken to compute the determinant of a square matrix of size j is , find upper bound on the

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Mathematics for Data Science, Solution Repository Linear Algebra, Mathematics for Data Science, Matrix Problems, MFDS, Operation Count, Rank of a Matrix, Upper Bound Leave a comment

The Gamma-Root Eigenvalue Problem

Posted 3 years ago by Ehan Ghalib

Question Let γ be the real root of a polynomial equation of degree 9 with integer coefficients. Construct the matrix     With this information, is it possible to i)

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Mathematics for Data Science, Solution Repository Eigenvalues, Linear Algebra, Mathematics for Data Science, Matrix, MFDS Leave a comment

Minimum Distance from A Parabola

Posted 3 years ago by Ehan Ghalib

Question Find the minimum distance from (4,2) to the parabola Solution Conceptually, this can be done by: 1) Considering the curve and finding the tangent. 2) Find normal to that

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Mathematics for Data Science, Solution Repository Distance from Curve, Equation of Tangent, Mathematics for Data Science, MFDS, Minimum Distance, Normal line Equation Leave a comment

Prove Eigenvalues < 1 for a Diminishing Matrix

Posted 3 years ago by Ehan Ghalib

Question Prove that if A is a square matrix of size , then as if and only if Solution Norm is a value that indicates the magnitude of a matrix.

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Mathematics for Data Science, Solution Repository Diminishing Matrix, Eigenvalues, Mathematics for Data Science, Matrix Problems, MFDS, Spectral Radius Leave a comment

Find Eigenvalues of Variable Matrix Using Properties

Posted 3 years ago by Ehan Ghalib

Question Given the following matrix     where c and r are arbitrary real numbers and 5.5 < r ≤ 6.5, and the fact that = 3 is one of

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Mathematics for Data Science, Solution Repository Eigenvalues, Linear Algebra, Mathematics for Data Science, Matrix Problems, MFDS Leave a comment

Problem to Preserve Non-Singularity of a Matrix

Posted 3 years ago by Ehan Ghalib

Question Let be a non-singular matrix. If column is replaced by a and that the resulting matrix is called along with , then state the necessary and sufficient condition for

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Mathematics for Data Science, Solution Repository Linear Algebra, Linear Independence, Mathematics for Data Science, Matrix Problems, MFDS, Non-Singular Matrix Leave a comment
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