1. Find the orthogonal projection of the matrix
[[3,2][4,5]] onto the space of diagonal 2x2 matrices...
1. Find the orthogonal projection of the matrix
[[3,2][4,5]] onto the space of diagonal 2x2 matrices of the form
lambda?I.
[[4.5,0][0,4.5]] [[5.5,0][0,5.5]] [[4,0][0,4]] [[3.5,0][0,3.5]] [[5,0][0,5]] [[1.5,0][0,1.5]]
2. Find the orthogonal projection of the matrix
[[2,1][2,6]] onto the space of symmetric 2x2 matrices of trace
0.
[[1,3][3,1]] [[1.5,1][1,1.5]] [[0,4][4,0]] [[3,3.5][3.5,3]] [[0,1.5][1.5,0]] [[2,1.5][1.5,2]] [[0.5,4.5][4.5,0.5]] [[1,6][6,1]] [[0,3.5][3.5,0]] [[1.5,3.5][3.5,1.5]]
3. Find the orthogonal projection of the matrix
[[1,5][1,2]] onto the space of antisymmetric 2x2
matrices.
[[0,1] [1,0]] [[0,2] [2,0]] [[0,1.5]
[1.5,0]] [[0,2.5] [2.5,0]] [[0,0]
[0,0]] [[0,0.5] [0.5,0]] [[0,1] [1,0]]
[[0,1.5] [1.5,0]] [[0,2.5]
[2.5,0]] [[0,0.5] [0.5,0]]
4. Let p be the orthogonal projection of
u=[40,9,91]T onto the...
Find an example of a nonzero, nonInvertible 2x2 matrix A and a
linearly independent set {V,W}...
Find an example of a nonzero, nonInvertible 2x2 matrix A and a
linearly independent set {V,W} of two, distinct
nonzero vectors in R2 such that
{AV,AW} are distinct, nonzero and
linearly dependent. verify the matrix A in noninvertible, verify
the set {V,W} is linearly independent and verify
the set {AV,AW} is linearly
dependent
. Enlarge each of the following linearly independent subsets T
of R5 to a basis B...
. Enlarge each of the following linearly independent subsets T
of R5 to a basis B for R5 containing T :
(a) T {[1,3, 0, 1, 4],[2, 2, 1,3, 1]}
(b) T {[1, 1, 1, 1, 1],[0, 1, 1, 1, 1],[0, 0, 1, 1, 1]}
(c) T {[1, 0,1, 0, 0],[0, 1,1, 1, 0],[2, 3,8,1, 0]}
Which of the following sets are linearly independent?
A. { (1, 0) , (1, 1) ,...
Which of the following sets are linearly independent?
A. { (1, 0) , (1, 1) , (11) } in R2
B. { (1, 1, 1), (1,1, 1), (1, 1, 1) } in R3
C. { 1 + x, x, 2 + 3x } in P2
D. { [1 1 , [1 1
0 0] , 0 1] } in
M22
Select from the following:
1. Only A and C.
2. Only B.
3. Only D.
4. Only B and...
1. Two dice are rolled. There are 36 possible outcomes, the
sample space is:
(1,1) (1,2)...
1. Two dice are rolled. There are 36 possible outcomes, the
sample space is:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4)
(2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3)
(4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2)
(6,3) (6,4) (6,5) (6,6)
A = ‘second roll is a 6’
B = ‘sum of two dice equals 7’
C = ‘sum of two dice equals 3’
a. What is P(BA)?
b. What is...
Question 1: Roll two fair dice. Then the sample space S is the
following.
S =...
Question 1: Roll two fair dice. Then the sample space S is the
following.
S =
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Let E be the event that the sum of the dice is odd, let F be the
event that the first die lands on 1,
and let G...
Decide whether the following set of vectors are linearly
independent or dependent. Justify the answer!
a)...
Decide whether the following set of vectors are linearly
independent or dependent. Justify the answer!
a) In R^3: v1=(0,2,3), v2=(3,1,4), v3=(3,2,2)
b) In R^3: u1=(1,2,0), u2=(2,1,3), u3=(4,2,1), u4=( 2,1,4)
c) In Matriz 2x2: A=  1 6  B=  1 4  C=  1 4

1 4 ,  3 2 ,  2 4 
2. Consider a tensided die of which the sides display the
numbers 1, 2, 3, and...
2. Consider a tensided die of which the sides display the
numbers 1, 2, 3, and 4 according to this table:
side of die 1 2 3 4 5 6 7 8 9 10 number displayed 1 1 1 1 2 2 2 3 3
4
Rolling two such dice is an experiment with the sample space S =
(1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4) (3,1)
(3,2) (3,3) (3,4) (4,1) (4,2) (4,3)...