TRUE OR FALSE?
There exists an invertible matrix that has 92 ones among its entries.
The statement is false.
A matrix will be non-invertible if it has identical rows.
An inverse of a matrix has an order,
The number of ones in inverse matrix, 92
A matrix will have 100 entries. If 92 among them are ones, then, there will be identical rows. Such identical rows cancel out each other. Then, the inverse of that matrix will not exist.
Hence, the given statement is false.
Let’s revisit the mini-Web with the graph
But here we consider the surfing model with a “jumping rate” of 20%, as discussed in Exercise 2.1.53. The corresponding transition matrix is
This transition matrix is positive and therefore regular, so that Theorem 2.3.11 applies. Use the power method (see Exercise 76) to find the equilibrium distribution. You may use technology. Write the components of as rational numbers.
Consider the regular tetrahedron sketched below, whose center is at the
Let T from to be the rotation about the axis through the points 0 and that transforms into . Find the images of the four corners of the tetrahedron under this transformation.
Let L from to be the reflection about the plane through the points 0 , . Find the images of the four corners of the tetrahedron under this transformation.
Describe the transformations in parts (a) through (c) geometrically.
d. Find the images of the four corners under the transformations . Are the two transformations the same?
e. Find the images of the four corners under the transformation . Describe this transformation geometrically
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