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Problem #6 from pg.115 and problem #2 from pg.121.
#6, pg.115: Determine if the following matrix is invertible or not:
[1−3−6043−360].
Solution: We compute the reduced echelon form
[1−3−6043−360]r2↔r3∼[1−3−6−360043]r∗2=r2+3r1∼[1−3−60−3−18043]r∗1=r1−r2r∗3=r3+43r2∼[10120−3−1800−21]r∗1=r1+1221r3r∗2=r2−1821r3∼[1000−3000−21]r∗2=−13r2r∗3=−121r3∼[100010001].
Hence we see by Theorem 8, pg.112 (a) and (b) that the given matrix is invertible.
Note: there are many ways to do this problem using the Invertible Matrix Theorem!
#2, pg.121: Compute the product of the following block matrices:
[E00F][PQRS].
Solution: Compute as if it were normal matrix multiplication:
[E00F][PQRS]=[EPEQFRFS].
