# MATHS----Matrix

For a given square matrix A the predicted values of matrix B are:

predicted B=A(A'A)^(-1)A'B

why is the matrix C=A(A'A)^(-1)A' an idempotent and symmetric matrix? and is this matrix invertible?

1. 👍 0
2. 👎 0
3. 👁 153
1. Assuming (A'A) is invertible, then (A'A)-1 exists.

A(A'A)-1A'
By the property of inverse of product of matrices,
(A'A)-1
=A-1 A'-1

Therefore
C=A(A'A)-1A'
=A(A-1 A'-1)A'
=(A A-1) (A'-1A')
= (I) (I)
=I
after application of associativity and the properties of inverse of matrices.
Since I is idempotent and invertible, so is C.

1. 👍 0
2. 👎 0
posted by MathMate
2. The equation of the parabola which contains 2 points (1,1) and (-2,-2) and whose tangent at the point (1,1) has the slope k is y=1/3(A)x^2+1/3(B)x-2/3(C) Express A,B and C with k.Please solve this problem.please

1. 👍 0
2. 👎 0

## Similar Questions

1. ### science

1 A ……... is a rectangular array of numbers that are enclosed within a bracket . horizontal set vertical matrix 2 When the numbers of rows is equal to the numbers of columns equal to 'n'. Where m=n. Then is

asked by sunday on March 15, 2014
2. ### math,algebra II

I have to work with these types of problems dealing with matrises can someone show me how to solve them.Heres one of them: Directions: Find the values of the variables in each equation in the first matrix it looks like this a+2

asked by jas on June 6, 2007
3. ### Math

Hi! I need help with these two questions. Thanks! :) 1.) Can we multiply the Matrix A (which is 3 x 4 matrix) by the other matrix, Matrix B (which is 3 x 4 matrix)? True Or False? 2.) When we multiply the 6 x 3 matrix by the 3 x 1

asked by Emily on March 26, 2015
4. ### algebra

When i have a matrix 4 X 4 and i have to multiply it by a 4 X 3 i know that the product size has to be a 4x 3 so do i do a row times column or how ? It's easiest to learn using the notations for tensors. For any matrix X denote

asked by student on June 17, 2007
5. ### Linear Algebra

Hi, I really need help with these True/False questions: (a) If three vectors in R^3 are orthonormal then they form a basis in R^3. (b) If Q is square orthogonal matrix such that Q^2018 = I then Q^2017 = Q^T. (c) If B is square

asked by Matt on March 26, 2017
6. ### Algebra

Given the following vector X, find a non-zero square matrix A such that AX=0: You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. X= 2 -8 6 A= _ _ _ _ _ _ _ _ _ Please help, I

asked by sal on October 13, 2018
7. ### Math

Fine the size of the following matrix and its additive inverse matrix. Identify if it is a square, column, or row matrix: [ 2 -3 7 1 0 4 ]

asked by Jeff on November 25, 2010
8. ### Math

Given the following matrix A, find an invertible matrix U so that UA is equal to the reduced row-echelon form of A: You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. A = 3 3

asked by valarie on October 21, 2018
9. ### Math

I have a few questions about T-Matrix. In excel, I am suppose to work with powered matrices to construct a weighted T matrix, using a scalar of .7. Does this mean I multiply each of the powered matrices by .7? Or do I power the

asked by Lisa on October 13, 2010
10. ### linear algebra

3. Suppose A is symmetric positive definite and Q is an orthogonal matrix (square with orthonormal columns). True or false (with a reason or counterexample)? a) (Q^(T))AQ is a diagonal matrix b) (Q^(T))AQ is a symmetric positive

asked by michael on December 1, 2010

More Similar Questions