19. Block Matrices • Prove that the determinant of a block matrix: A B 0 D . is det(A) · det (D), where A and D are square matrices. • Show how block matrices are used in solving large-scale linear systems.
19. Block Matrices • Prove that the determinant of a block matrix: A B 0 D . is det(A) · det (D), where A and D are square matrices. • Show how block matrices are used in solving large-scale linear systems.
Chapter7: Systems Of Equations And Inequalities
Section7.8: Solving Systems With Cramer's Rule
Problem 3SE: Explain what it means in terms of an inverse for a matrix to have a 0 determinant.
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![19. Block Matrices
• Prove that the determinant of a block matrix:
A B
0 D
.
is det(A) · det (D), where A and D are square matrices.
•
Show how block matrices are used in solving large-scale linear systems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6527c97f-bcd7-44bb-a52a-9c5764f88724%2Fc227de74-1730-4763-b94b-8b2f7d1a29cd%2Fhqo4nb8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:19. Block Matrices
• Prove that the determinant of a block matrix:
A B
0 D
.
is det(A) · det (D), where A and D are square matrices.
•
Show how block matrices are used in solving large-scale linear systems.
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