Problem 3. A shear transformation parallel to the x-axis can defined by a matrix S such that Sî î mî +ĵ. Here m is a number, called the shear factor. This is illustrated by the following picture, when m = Sj = }i+j î Sî = î Shear transformations are used in fluid dynamics, to describe fluid flow near the boundary of a channel. a. Find the matrix S, if m = . b. Let L be the line y = 2x. Find a matrix S which defines a shear parallel to L, with shear factor .
Problem 3. A shear transformation parallel to the x-axis can defined by a matrix S such that Sî î mî +ĵ. Here m is a number, called the shear factor. This is illustrated by the following picture, when m = Sj = }i+j î Sî = î Shear transformations are used in fluid dynamics, to describe fluid flow near the boundary of a channel. a. Find the matrix S, if m = . b. Let L be the line y = 2x. Find a matrix S which defines a shear parallel to L, with shear factor .
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b) translation:
"Find a matrix S transpose which defines a shear parallel to L, with shear factor 1/2"
Transcribed Image Text:Problem 3. A shear transformation parallel to the x-axis can defined by a matrix S such that
Sî
î
mî + ĵ.
Here m is a number, called the shear factor. This is illustrated by the following picture, when m =
Sj = }î+ĵ
L.
î
Sî = î
Shear transformations are used in fluid dynamics, to describe fluid flow near the boundary of a channel.
1
a. Find the matrix S, if m =
2.
b. Let L be the line y
2x. Find a matrix S which defines a shear parallel to L, with shear factor .
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