Find R = A + B, given that A has magnitude 4 and is at an angle of 30° above the positive x-axis and B has magnitude 2 and is at an angle of 55° above the positive x-axis.
Find R = A + B, given that A has magnitude 4 and is at an angle of 30° above the positive x-axis and B has magnitude 2 and is at an angle of 55° above the positive x-axis.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please Ans 6 only handwritten .
![1. Suppose an n x n matrix A satisfies the equation A²-2A+1=0. Show that A³ = 3A-21 and
A4-4A-31
2. Let A be the following Matrix:
• Compute the matrices A2, AAT and A-¹.
Find the numbers p and q such that A²=pA+ql, where I is the 2x2 identity matrix.
. Let B=A-tl, where t is a scalar. For which value of t is B not invertible?
3. Determine if b is a linear combination of the vectors a₁, az and as where
5
a1=
a.
a2=
b.
If b is a linear combination of the vectors a₁, a2 and a3, express b as linear combination of
the vectors a₁, a2 and a3.
C.
4. Normalize the following vectors:
a) u =(3,-4)
b) v (4, -2, -3, 8)
c) w = (1/2, 2/3, -1/4)
5. Determine whether the given matrix is singular or nonsingular. If it is nonsingular, find
its inverse
6
3
,a3=
1
0
3
b=
2
-4 2
-1
5
4
2
2
1
-1 -2
ol
6. Find R = A + B, given that A has magnitude 4 and is at an angle of 30° above the positive
x-axis and B has magnitude 2 and is at an angle of 55° above the positive x-axis.
7. A plane flies with a velocity of 52 m/s east through a 12 m/s cross wind blowing the
plane south. Find the magnitude and direction (relative to due north) of the resultant
velocity at which it travels.
8. If A = (4, 2, -1) and B = (2, -6, -3) then calculate a vector that is perpendicular to both A
and B
[2³3]
311100
(1-A)(1+A+A²)
9. Find the inverse of matrix C= 4
1 -2 1
-7 3
-2 6 -4
[0
0 01
10. Let A 1 0 0. Show that A³-0. Use matrix algebra to compute the product of
Lo
1 ol](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23053f65-a312-4931-a9ce-354bb355339d%2Fa81a6b3a-10dc-4f3f-90e8-80f678ff6304%2F0b53lzr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Suppose an n x n matrix A satisfies the equation A²-2A+1=0. Show that A³ = 3A-21 and
A4-4A-31
2. Let A be the following Matrix:
• Compute the matrices A2, AAT and A-¹.
Find the numbers p and q such that A²=pA+ql, where I is the 2x2 identity matrix.
. Let B=A-tl, where t is a scalar. For which value of t is B not invertible?
3. Determine if b is a linear combination of the vectors a₁, az and as where
5
a1=
a.
a2=
b.
If b is a linear combination of the vectors a₁, a2 and a3, express b as linear combination of
the vectors a₁, a2 and a3.
C.
4. Normalize the following vectors:
a) u =(3,-4)
b) v (4, -2, -3, 8)
c) w = (1/2, 2/3, -1/4)
5. Determine whether the given matrix is singular or nonsingular. If it is nonsingular, find
its inverse
6
3
,a3=
1
0
3
b=
2
-4 2
-1
5
4
2
2
1
-1 -2
ol
6. Find R = A + B, given that A has magnitude 4 and is at an angle of 30° above the positive
x-axis and B has magnitude 2 and is at an angle of 55° above the positive x-axis.
7. A plane flies with a velocity of 52 m/s east through a 12 m/s cross wind blowing the
plane south. Find the magnitude and direction (relative to due north) of the resultant
velocity at which it travels.
8. If A = (4, 2, -1) and B = (2, -6, -3) then calculate a vector that is perpendicular to both A
and B
[2³3]
311100
(1-A)(1+A+A²)
9. Find the inverse of matrix C= 4
1 -2 1
-7 3
-2 6 -4
[0
0 01
10. Let A 1 0 0. Show that A³-0. Use matrix algebra to compute the product of
Lo
1 ol
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