Question 2. True or false
2. If [T]β is the matrix representing the linear map T in the
basis β, then the jth column of [T]β contain the coordinates of the
T(βj) in the basis β, and same for the rows.
(3) Write elimination matrix representing each step in
elimination process. ( not augmented matrix)
(a)
2x + y − z = 3
x + 3y − z = 6
3x − y + 7z = 8
b)
x+y−z−t=0
x + y + 2z − t = 3
2x + 2y + z + 3t = 13
x + 2y + 5z − 7t = 3
Find the matrix P that diagonalizes A, and check your
work by computer P^-1AP. This matrix is
[-14 12]
[-20 17]
I've tried this problem, and I keep getting the eigenvalues of
λ=1, 2 and the eigenspace [4 5] for λ=1, and eigenspace [3 4] for
λ=2. However, whenever I check it with P^-1AP, it doesn't produce a
diagonal matrix.
In Java please You are given a matrix of characters representing
a big box. Each cell of the matrix contains one of three
characters: " / "which means that the cell is empty; '*', which
means that the cell contains an obstacle; '+', which means that the
cell contains a small box. You decide to rotate the big box
clockwise to see how the small boxes will fall under the gravity.
After rotating, each small box falls down until it...
1. For each matrix A below compute the characteristic polynomial
χA(t) and do a direct matrix computation to verify that χA(A) =
0.
(4 3
-1 1) (2 1 -1 0 3 0 0 -1 2) (3*3 matrix)
2. For each 3*3 matrix and each eigenvalue below
construct a basis for the eigenspace Eλ.
A= (9 42 -30 -4 -25 20 -4 -28 23),λ = 1,3
A= (2 -27 18 0 -7 6 0 -9 8) , λ = −1,2...
In each case, determine a 3 × 3 matrix ? that fits the
description. Justify that the conditions are met in each case.
(a) Matrix ? has rank 1 and ? + ? is not invertible.
(b) Matrix A is symmetric and the null space of ? is a
point.
for each matrix A below, describe the invariant subspaces for
the induced linear operator T on F^2 that maps each v set of F^2 to
T(v)=Av. (a) [4,-1;2,1], (b) [0,1;-1,0], (c) [2,3;0,2], (d)
[1,0;0,0]
Suppose you have one data set with 30 cases, each case
representing a student in this class. The following variables are
available: age, gender/sex, race/ethnicity, class (freshman,
sophomore, etc.), and GPA.
For each of the 5 variables, explain (1) the level of
measurement and (2) the measures of central tendency available to
them.
Race:
Gender/sex:
Race/ethnicity:
Class:
GPA: