PROBLEMS For Problems 17-26, find the change-of-basis matrix P C ← B from the given ordered basis B to the given ordered basis C of the vector space V . V = ℝ 2 ; B = { ( − 5 , − 3 ) , ( 4 , 28 ) } ; C = { ( 6 , 2 ) , ( 1 , − 1 ) } .
PROBLEMS For Problems 17-26, find the change-of-basis matrix P C ← B from the given ordered basis B to the given ordered basis C of the vector space V . V = ℝ 2 ; B = { ( − 5 , − 3 ) , ( 4 , 28 ) } ; C = { ( 6 , 2 ) , ( 1 , − 1 ) } .
For Problems 17-26, find the change-of-basis matrix
P
C
←
B
from the given ordered basis
B
to the given ordered basis
C
of the vector space
V
.
V
=
ℝ
2
;
B
=
{
(
−
5
,
−
3
)
,
(
4
,
28
)
}
;
C
=
{
(
6
,
2
)
,
(
1
,
−
1
)
}
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Ex. 600. Given the 2x2 Matrix A
1 2
11 3
Determine B=A+A and C=A-A
Answers:
B(1,1),B(1,2),B(2,1),B(2,2),C(1,1),C(1,2),C(2,1),C(2,2)
Ex. 610. Given the 2x2 Matrix A
4 1
5 3
Determine B=A*A
Answers: B(1,1),B(1,2),B(2,1),B(2,2) ans:4
Ex. 615. Given the 2x2 Matrix A
43
15
Determine B=transpose(A). Answers:
B(1,1),B(1,2),B(2,1), and B(2,2) ans:4
1. In each part of this question, you have been given a system of equations and the corresponding matrix
taken to RREF.
Write the general solution as a vector equation.
• List the basic solutions.
a.
b.
(x₁ - x₂ + 2x4 = 0
[1
-X₁ + x₂ + 3x3 - 11x4
0
2x₁ - 2x₂ + 4x4
0
0
-4x₁ + 4x₂ + 3x3 - 17x4 = 0 Lo
-
= 0
"
-1 0
2 01
0 1 -3 0
0
0
0
0
0
00
(3w+9y15z = 0
1
0
-14w + 33x - 75y - 62z = 0
0 1
-5w+ 14x - 29y - 31z = 0
0
0
(52w 164x + 320y + 396z = 0 Lo
0
3
-1 -4
0
0
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Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY