Linear algebra: please solve q3 and 7 correctly and handwritten In Exercises 1-4, verify that B is the inverse of A byshowing that AB = BA = 1.1. A =2. A =3. A =4. A =7 45 33 102 10B =0021034 1B =-1 -2 111 3 -150-15"3-47-5B =1 -13-.2B =-20135545-4In Exercises 5-8, use the appropriate inverse matrixfrom Exercises 1-4 to solve the given system of linearequations.5. 3x1 + 10x2=62x1 + 10x2 = 97.x2 + 3x3 = 45x1 + 5x2 + 4x3 = 2x₁ + x₂ + x3 = 29. A =6. 7x1 + 4x2 = 55x1 + 3x2= 23 2 18.In Exercises 9-12, verify that the given matrix A doesnot have an inverse. [Hint: One of AB= I or BA = Ileads to an easy contradiction.]00X1= 2-2x1 + x₂= 35x₁4x2 + x3 = 210. A =0420170 39

We will solve question no. 3 and question no. 7

Answered: In Exercises 1-4, verify that B is the…

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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Linear algebra: please solve q3 and 7 correctly and handwritten

In Exercises 1-4, verify that B is the inverse of A by
showing that AB = BA = 1.
1. A =
2. A =
3. A =
4. A =
7 4
5 3
3 10
2 10
B =
00
210
34 1
B =
-1 -2 11
1 3 -15
0-1
5
"
3-4
7
-5
B =
1 -1
3
-.2
B =
-2
013
554
5-4
In Exercises 5-8, use the appropriate inverse matrix
from Exercises 1-4 to solve the given system of linear
equations.
5. 3x1 + 10x2=6
2x1 + 10x2 = 9
7.
x2 + 3x3 = 4
5x1 + 5x2 + 4x3 = 2
x₁ + x₂ + x3 = 2
9. A =
6. 7x1 + 4x2 = 5
5x1 + 3x2= 2
3 2 1
8.
In Exercises 9-12, verify that the given matrix A does
not have an inverse. [Hint: One of AB= I or BA = I
leads to an easy contradiction.]
00
X1
= 2
-2x1 + x₂
= 3
5x₁4x2 + x3 = 2
10. A =
042
017
0 39

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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