The matrix M represents a linear transformation of two-dimensional space and det(M)= 4. What can be said about the area of a region in the plane compared to the area that it is sent to under the transformation? The area of the region quadruples. O The area of the region is one-half as large. O The area of the region is one-fourth as large.
The matrix M represents a linear transformation of two-dimensional space and det(M)= 4. What can be said about the area of a region in the plane compared to the area that it is sent to under the transformation? The area of the region quadruples. O The area of the region is one-half as large. O The area of the region is one-fourth as large.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The matrix M represents a linear transformation of two-dimensional space and det(M) = 4. What can be said about the area of a region in the plane compared to the area that it is sent to under the transformation?
The area of the region quadruples.
The area of the region is one-half as large.
The area of the region is one-fourth as large.
The area of the region doubles.
The linear transformation T sends all of three-dimensional space to a line. What can you say about the value of the determinant of the matrix representing the transformation?
O The determinant is 0.
O The determinant is negative.
O The absolute value of the determinant is less than 1.
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