Linear algebra: please solve q4 and 7 correctly and handwritten
Transcribed Image Text: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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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F624dcfab-19f1-4c4b-b3ec-94b9a5b18d08%2Fa8d4b90d-b207-408c-b359-9e5ca48d6894%2Fkz8hpaa_processed.jpeg&w=3840&q=75)
