Use R code Create a vector V with 8 elements (7,2,1,0,3,-1,-3,4): Transform that vector into a...

Use R code

Create a vector V with 8 elements (7,2,1,0,3,-1,-3,4):

Transform that vector into a rectangular matrix A of dimensions 4X2 (4- rows, 2-columns);
Create a matrix transpose to the above matrix A. Call that matrix AT;
Calculate matrix products: A*AT and AT*A. Present the results. What are the dimensions of those two product matrices;
Square matrixes sometimes have an inverse matrix. Try calculating inverse matrices (or matrixes, if you prefer) of above matrices (matrixes) A*AT and AT*A;
Extend the above vector V with the ninth number of value -2. Do it elegantly by concatenating two vectors!;
Transform that extended vector into a 3X3 matrix B.
Calculate the inverse matrix of matrix B. Call it Binv. Demonstrate that the product of B and Binv is the same as the product of Binv and B and is equal to what?
Determine the eigenvectors of matrixes B;
Construct a new matrix C which is made by using each eigenvector of matrix B as a column. Calculate the product of matrix C and matrix B and the product of matrix B and C. Is there any significance to the elements of the product matrixes;
Transform matrix B into a matrix with names columns and named rows;
Transformed that fully “named” matrix into a data.frame;
Ask the object you just created what is its class().

Expert Solution

orchestra answered 3 years ago

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