Please Ans 10 only handwritten . 1. Suppose an n x n matrix A satisfies the equation A²-2A+1=0. Show that A³ = 3A-21 andA4-4A-312. 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 where5a1=a.a2=b.If b is a linear combination of the vectors a₁, a2 and a3, express b as linear combination ofthe 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, findits inverse63,a3=103b=2-4 2-154221-1 -2ol6. Find R = A + B, given that A has magnitude 4 and is at an angle of 30° above the positivex-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 theplane south. Find the magnitude and direction (relative to due north) of the resultantvelocity at which it travels.8. If A = (4, 2, -1) and B = (2, -6, -3) then calculate a vector that is perpendicular to both Aand B[2³3]311100(1-A)(1+A+A²)9. Find the inverse of matrix C= 41 -2 1-7 3-2 6 -4[00 0110. Let A 1 0 0. Show that A³-0. Use matrix algebra to compute the product ofLo1 ol

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Answered: [0 0 01 10. Let A=100. Show that A³=0.…

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[0 0 01 10. Let A=100. Show that A³=0. Use matrix algebra to compute the product of Lo 1 ol (1-A)(1+A+A²)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.7: The Inverse Of A Matrix

Problem 32E

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Question

Please Ans 10 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

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