Question 3, Exercise 2.3
Solutions of Question 3 of Exercise 2.3 of Unit 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.
Question 3(i)
Find the ranks of the matrix. [10−2221−123]
Solution
[10−2221−123]R∼[10−2025021] by R2−2R1 and R1−2R3R∼[10−2004021] by R2−R3 The last matrix is the echelon form of given matrix having 3 non-zero rows.
Hence rank of given matrix is 3.
Question 3(ii)
Find the ranks of the matrix. [31−40211−1−2]
Solution
[31−40211−1−2]R∼[1−1−202131−4] by R1↔R3R∼[1−1−2021042] by R3−3R1R∼[1−1−2021000] by R3−2R2 The last matrix is the echelon form of given matrix having 2 non-zero rows.
Hence rank of the given matrix is 2.
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