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,...
Related questions
Question
Determine whether the statement are TRUE or FALSE. Write TRUE if the Statement is True and False otherwise.
![36. In a symmetric n x n matrix, the (i,j)- and (j, i)-entries
are equal for all i = 1,2,...n and j = 1,2,..,n.
37. The determinant of a matrix is a matrix of the same size.
а
38. det
= ad + bc.
39. If the determinant of a 2 x 2 matrix equals zero, then the
matrix is invertible.
40. If a 2 x 2 matrix is invertible, then its determinant equals
zero.
41. If B is a matrix obtained by multiplying each entry of
some row of a 2 × 2 matrix A by the scalar k, then
det B = k det A.
42. For n > 2, the (i,j)-cofactor of an n x n matrix A is the
determinant of the (n – 1) × (n – 1) matrix obtained by
deleting row i and column j from A.
43. For n > 2, the (i,j)-cofactor of an n x n matrix A equals
(-1)i+j times the determinant of the (n – 1) × (n – 1)
matrix obtained by deleting row i and column j from A.
44. The determinant of an n x n matrix can be evaluated by
a cofactor expansion along any row.
45. Cofactor expansion is an efficient method for evaluating
the determinant of a matrix.
46. The determinant of a matrix with integer entries must be
an integer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b0dd486-c065-4c38-b7eb-8d57a461ff0e%2F8874be05-d08b-4920-b708-8c186148a728%2Ftc6jpdm_processed.png&w=3840&q=75)
Transcribed Image Text:36. In a symmetric n x n matrix, the (i,j)- and (j, i)-entries
are equal for all i = 1,2,...n and j = 1,2,..,n.
37. The determinant of a matrix is a matrix of the same size.
а
38. det
= ad + bc.
39. If the determinant of a 2 x 2 matrix equals zero, then the
matrix is invertible.
40. If a 2 x 2 matrix is invertible, then its determinant equals
zero.
41. If B is a matrix obtained by multiplying each entry of
some row of a 2 × 2 matrix A by the scalar k, then
det B = k det A.
42. For n > 2, the (i,j)-cofactor of an n x n matrix A is the
determinant of the (n – 1) × (n – 1) matrix obtained by
deleting row i and column j from A.
43. For n > 2, the (i,j)-cofactor of an n x n matrix A equals
(-1)i+j times the determinant of the (n – 1) × (n – 1)
matrix obtained by deleting row i and column j from A.
44. The determinant of an n x n matrix can be evaluated by
a cofactor expansion along any row.
45. Cofactor expansion is an efficient method for evaluating
the determinant of a matrix.
46. The determinant of a matrix with integer entries must be
an integer.
![47. The determinant of a matrix with positive entries must be
positive.
48. If some row of a square matrix consists only of zero
entries, then the determinant of the matrix equals zero.
49. An upper triangular matrix must be square.
50. A matrix in which all the entries to the left and below
the diagonal entries equal zero is called a lower triangular
matrix.
51. A 4 x 4 upper triangular matrix has at most 10 nonzero
entries.
52. The transpose of a lower triangular matrix is an upper
triangular matrix.
53. The determinant of an upper triangular n x n matrix or a
lower triangular n xn matrix equals the sum of its diag-
onal entries.
54. The determinant of I, equals 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b0dd486-c065-4c38-b7eb-8d57a461ff0e%2F8874be05-d08b-4920-b708-8c186148a728%2Fn2l5bek_processed.png&w=3840&q=75)
Transcribed Image Text:47. The determinant of a matrix with positive entries must be
positive.
48. If some row of a square matrix consists only of zero
entries, then the determinant of the matrix equals zero.
49. An upper triangular matrix must be square.
50. A matrix in which all the entries to the left and below
the diagonal entries equal zero is called a lower triangular
matrix.
51. A 4 x 4 upper triangular matrix has at most 10 nonzero
entries.
52. The transpose of a lower triangular matrix is an upper
triangular matrix.
53. The determinant of an upper triangular n x n matrix or a
lower triangular n xn matrix equals the sum of its diag-
onal entries.
54. The determinant of I, equals 1.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra And Trigonometry (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780135163078/9780135163078_smallCoverImage.gif)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
![Introduction to Linear Algebra, Fifth Edition](https://www.bartleby.com/isbn_cover_images/9780980232776/9780980232776_smallCoverImage.gif)
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
![College Algebra (Collegiate Math)](https://www.bartleby.com/isbn_cover_images/9780077836344/9780077836344_smallCoverImage.gif)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education