Let D be a 4 × 4 matrix of the following form: [a11 a12 b11 b12 a21 a22 b21 b22 D = 0 0 C11 C12 0 0 C21 C22 That is D is "built up" of the four 2×2 matrices consisting of the together with a 2 × 2 matrix of 0's. aij bij and Cij coefficients, Show that: det (D) = det (La a11 a12 C12 a21 a22 C21 C22

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 63EQ
Question
Let D be a 4 x 4 matrix of the following form:
D:
a11
a12 b11 b12
a21 a22 b21 b22
0 C11 C12
0 0 C21 C22
That is D is "built up" of the four 2 × 2 matrices consisting of the
together with a 2 × 2 matrix of 0's.
dij,
bij and
Cij
coefficients,
Show that:
a11
a12
C12
det (D) = det
a21
a22
C21
C22
Transcribed Image Text:Let D be a 4 x 4 matrix of the following form: D: a11 a12 b11 b12 a21 a22 b21 b22 0 C11 C12 0 0 C21 C22 That is D is "built up" of the four 2 × 2 matrices consisting of the together with a 2 × 2 matrix of 0's. dij, bij and Cij coefficients, Show that: a11 a12 C12 det (D) = det a21 a22 C21 C22
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,