3. Let A, B and C be matrices defined by 17 9 -- -- -- -- 1 3 5 1 4) A 8 2 7 B = C D 4 (-) 1 4 9, 2 -1 -3. Calculate the following expressions or give reason why they are not defined, 4 -$). -5 1 -1 =(2²+²7) 9 6

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 51EQ
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3rd question
1. Use Gaussian elimination with back substitution or Gauss-Jordan to solve:
2x + 2y + z = 10
-x + 3y + 4z = 0
3x - y + 6z = 12
2. Consider the following vectors a and b as shown in Figure below.
Sketch the following vectors:
(a) a + b (b) a − b (c) 3a (d) -b (e) 3a-b
3. Let A, B and C be matrices defined by
9 4
3
-1
b
17
A = 8
-- -- -- --
B = 1
C
2
5 1 4
2 7
-5
1 4 9,
-3,
Calculate the following expressions or give reason why they are not defined,
(a) A + B
(c) AD
(d) AB
4. Let u =
(a) u v
"
-1
3
2
(b) ||v||
(b) AC
and v =
-1
=(²2+²7)
-2
(¹)
1 be vectors in R³. Evaluate
5
(c) d(u, v)
(d) ||v + u||²
Transcribed Image Text:1. Use Gaussian elimination with back substitution or Gauss-Jordan to solve: 2x + 2y + z = 10 -x + 3y + 4z = 0 3x - y + 6z = 12 2. Consider the following vectors a and b as shown in Figure below. Sketch the following vectors: (a) a + b (b) a − b (c) 3a (d) -b (e) 3a-b 3. Let A, B and C be matrices defined by 9 4 3 -1 b 17 A = 8 -- -- -- -- B = 1 C 2 5 1 4 2 7 -5 1 4 9, -3, Calculate the following expressions or give reason why they are not defined, (a) A + B (c) AD (d) AB 4. Let u = (a) u v " -1 3 2 (b) ||v|| (b) AC and v = -1 =(²2+²7) -2 (¹) 1 be vectors in R³. Evaluate 5 (c) d(u, v) (d) ||v + u||²
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