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.

Find the ranks of the matrix. [102221123]

[102221123]R[102025021] by R22R1 and R12R3R[102004021] by R2R3 The last matrix is the echelon form of given matrix having 3 non-zero rows.

Hence rank of given matrix is 3.

Find the ranks of the matrix. [314021112]

[314021112]R[112021314] by R1R3R[112021042] by R33R1R[112021000] by R32R2 The last matrix is the echelon form of given matrix having 2 non-zero rows.

Hence rank of the given matrix is 2.