Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Transcribed Image Text:1. By using back-substitution to solve the systems
a)
x - y = 4, 2y + z = 6, 3z = 6;
b)
-x + y – z = 0, y +z = 6, 2z = 4;
2. Solve the system of linear equation
x + y +z = 6, 2x – y + z = 3, 3x – z = 0;
3. Determine the values of k such that the following system of linear equation
does not have a unique solution
x+y+ kz = 3, x+ ky +z = 2, kx +y +z = 1;
4. Show that if ax? + bx +c= 0 for all x, then a = 6 = c= 0;
-1
5. Find the product of matrices A =
3
and B =
1.
-2
2
-1
-3
-2
6. Given the matrices
-1 1
1.
-2
2
3
A =
B =
3.
4
-1 5 1
Find 3A – 2B;
7. Given a square matrix
1
-2
A =
-3
-1
4
1
Find A? + 2A;
8. Solve the system using Gaussian elimination with back-substitution
x + 2y = 0, x + y = 6, 3x – 2y = 8;
9. Solve the system using Gauss-Jourdan elimination
x – 3z = -2, 3x + y – 2z = 5, 2x + 2y + z = 4;
10. Find the solution set of the system of linear equations represented by
the following augmented matrix
1
-1
3
1
-2
1
1
-1
![11. Find (if possible) conditions on a, b, and c such that the following system
of linear equation:
2x – y + z = a, x + 2y + z = b, 3y +3z = c
has (a) no solution, (b) exactly one solution, and (c) an infinite number of
solutions;
12. Solve for æ, y and z in the matrix equation
]-(.
4
4
+2
1
-1
-5
-x
13. Find AB – BA for the matrices
2
1.
1
-1
A =
-1
2
-3
B =
2
3
2
4
-2
14. Solve the following matrix equation for a, b, c, d,
1 3
2 4
a b
6
19
d
3
BA for the matrices
15. Find conditions on a, b, c and d such that AB =
below
a
1
1
A =
B =
d
16. Let
-1
A =
2
B =
3.
Show that AB = BA = I,, where I, is a 2 dimensional identity matrix, i.e.
1 0
0 1
17. Find the inverse of the matrix use an inverse matrix to solve each system
of
linear equations.
1 1
A =
3 5
-4
6.
5
18. Use an inverse matrix to solve the following system of linear equation
x1 + 2x2 + x3 = 2, x1 + 2x2 – x3 = 4, x1 – 2x2 + x3 = -2;
19. Use expansion by cofactor to find the determinant of the matrix
2 6 6 2
2 7 3 6
150 1
7 0
A =
3
+ "i](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec892432-ad3d-44c7-aaed-65f8ea23f103%2Fd718d221-d7f2-4b5e-beb7-bab4513563d2%2Fq8pgk6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:11. Find (if possible) conditions on a, b, and c such that the following system
of linear equation:
2x – y + z = a, x + 2y + z = b, 3y +3z = c
has (a) no solution, (b) exactly one solution, and (c) an infinite number of
solutions;
12. Solve for æ, y and z in the matrix equation
]-(.
4
4
+2
1
-1
-5
-x
13. Find AB – BA for the matrices
2
1.
1
-1
A =
-1
2
-3
B =
2
3
2
4
-2
14. Solve the following matrix equation for a, b, c, d,
1 3
2 4
a b
6
19
d
3
BA for the matrices
15. Find conditions on a, b, c and d such that AB =
below
a
1
1
A =
B =
d
16. Let
-1
A =
2
B =
3.
Show that AB = BA = I,, where I, is a 2 dimensional identity matrix, i.e.
1 0
0 1
17. Find the inverse of the matrix use an inverse matrix to solve each system
of
linear equations.
1 1
A =
3 5
-4
6.
5
18. Use an inverse matrix to solve the following system of linear equation
x1 + 2x2 + x3 = 2, x1 + 2x2 – x3 = 4, x1 – 2x2 + x3 = -2;
19. Use expansion by cofactor to find the determinant of the matrix
2 6 6 2
2 7 3 6
150 1
7 0
A =
3
+ "i
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