Chapter Ten — Applications of Matrix Algebra
The Humongous Book of Algebra Problems
Note: Problems 10.6–10.7 refer to matrix B deﬁned below.
10.7 Verify that B · D = B, assuming that D is the identity matrix identiﬁed in
Calculate the product of the matrices and verify that it is equal to B.
Matrix Row Operations
Swap rows, add rows, or multiply by a number
10.8 Identify the three elementary matrix row operations.
The three elementary row operations are: exchanging the positions of two rows,
multiplying a row by a nonzero number, and replacing a row by adding it to a
multiple of another row in the matrix.
Note: Problems 10.9–10.12 refer to matrix A deﬁned below.
10.9 Perform the row operation: .
The notation R
refers to the ith row of the matrix, so this problem refers to the
second row of A (R
), and the third row of A (R
). The symbol “ ” indicates
that the rows should be switched. To perform the row operation , move
the elements of the second row to the third row and vice versa.
For example, you
could swap the rst
two rows so that the
second row becomes
the rst and vice
This is the
trickiest of the
three row operations.
To see it in action,
look at Problems
10.11 and 10.12.