Matrix Operations and Vector Manipulation, Cheat Sheet of Law

Instructions for creating various matrices and vectors, including a 2x3 matrix m1 with all ones, a 3-element vector v1 with all ones, a 3x3 matrix m2 with diagonal entries of 5, and a 3x3 matrix m3 constructed from m1, m2, and v1. The document then describes how to create three vectors v2, v3, and v4 from the rows of m3, and how to alter specific entries in these vectors to create a new vector m4. This document could be useful for students studying linear algebra, matrix theory, or numerical methods, as it covers fundamental operations and manipulations with matrices and vectors, which are essential concepts in these fields.

Typology: Cheat Sheet

2023/2024

Uploaded on 03/31/2024

daniyal-shabbir
daniyal-shabbir 🇵🇰

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(a) Make a matrix M1 which consists of two rows and three columns and all the entries in the
matrix are ones.
(b) Make a vector V1 consisting of three ones.
(c) Make a 3x3 matrix M2 in which the diagonal entries are all fives.
(d) Now make a matrix M3 from M1, M2 and V1 which look like the matrix given below
M3=
1 1 1
1 1 1
0 0 0
5 0 0
0 5 0
0 0 5
(e) Now use the referencing element concept to make three vectors V2, V3 and V4 such that V2
consists of first row of M3, V3 consists of second row of M3 and V4 consists of third row of M3.
(f) Now alter the fourth entry of vectors V2, fifth entry of V3 and sixth entry of V4 to 1.4 and
make a new vector M4 which looks like the matrix given below.
M4=
1 1 1
1 1 1
0 0 0
1.4 0 0
0 1.4 0
0 0 1.4

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(a) Make a matrix M1 which consists of two rows and three columns and all the entries in the matrix are ones. (b) Make a vector V1 consisting of three ones. (c) Make a 3x3 matrix M2 in which the diagonal entries are all fives. (d) Now make a matrix M3 from M1, M2 and V1 which look like the matrix given below M3=

(e) Now use the referencing element concept to make three vectors V2, V3 and V4 such that V consists of first row of M3, V3 consists of second row of M3 and V4 consists of third row of M3. (f) Now alter the fourth entry of vectors V2, fifth entry of V3 and sixth entry of V4 to 1.4 and make a new vector M4 which looks like the matrix given below. M4=