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Material Type: Exam; Professor: Johnson; Class: INTRO LINEAR ALGEBRA; Subject: Mathematics; University: University of Maryland; Term: Unknown 1989;
Typology: Exams
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MATH 24O R. Johnson
[151 1. Let E =
fO 1 -2' 1 1 if 10 1 -
Oct. if,
Perform the following operations when possible. is not possible, explain why.
If an operation
(a) EF ( b ) FE 2 (c) (d)
[2O] Solve simultaneously the systems (a) x - 2 x 12
x = - 2 3 2x -5x ->- x = 1 123 3x - 7x 1 2
(b) x - 2 x + x 123 2x — 5x + x 1 Z 3 3x - 7x + 2x 123
E2O] (^3) Calculate the cofactor matrix of
A ='
37
Use this to compute adj<A) and A
-i
[151 if (^) Wha ondition on a , b , c will ei (^) e that this system is consistent?
x -»- 2y - 2z = a y + 5z = b 3x + 7y - z = c
[15] 5. Solve by Cramer's rule
x + 2x = it 2 3 2x + ifx + 3x = - 1 Z 3 3x + 7x + 6x 123 0
f. 15] 6. (a) Suppose A and B are invertible matrices. What is the formula for (AB)" 1?
(b) Give an example of two 2x2 e1ementary matrices A and B for which AB ^ BA.
(c) Suppose A is a square matrix which satisifes A + EA 31.
Show that A is invertible and A = ~ P~ + l~ I. J O
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