1 -1 0 1 Construct a 4 x2 matrix D, using only 1 and 0 as entries, such that AD = I2. Is it possible that CA 11 -1 ...

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.4: Transistion Matrices And Similarity
Problem 29E
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1
Construct a 4x2 matrix D, using only 1 and 0 as entries, such that AD = I2. Is it possible that CA =I4 for some 4 x2 matrix C? Explain.
Let A =
11 -1
...
D=
Transcribed Image Text:1 -1 0 1 Construct a 4x2 matrix D, using only 1 and 0 as entries, such that AD = I2. Is it possible that CA =I4 for some 4 x2 matrix C? Explain. Let A = 11 -1 ... D=
Expert Solution
Step 1

In the given question, the concept of the matrix is applied.

Matrix

A matrix is a rectangular array or table in which numbers or components are arranged in rows and columns. Matrices are the plural version of the matrix. Matrices can contain various columns and rows. Matrix addition, scalar multiplication, matrix multiplication, transposition, and other operations can be done on them. When conducting these matrix operations, certain rules must be followed, such as matrices can only be added or subtracted if they have the same number of rows and columns, and they can only be multiplied if the columns in the first and rows in the second are precisely the same.

 

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