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Check whether or not the matrix A=[1 1 1
0 - 2 2
0 - 2 - 3] is diagonalisable. If it is, find a matrix P, and a matrix D such that P^-1 AP=D. If A is not diagonalisable find AdjkA).
Solve the following equations using matrix algebra:

2x + y - z = 11

x - 2y + 2z = -2

3x - y + 3z = 5
solve the following equation using matrix algebra
2x+y-z=11
x-2y+2z=2
3x-y+3z=5
Solve the following equations using matrix algebra:

2x + y - z = 11

x - 2y + 2z = -2

3x - y + 3z = 5
Solve the following equations using matrix algebra:

2x + y - z = 11

x - 2y + 2z = -2

3x - y + 3z = 5
P(e)(x) = {p(x) ∈ R[x]|p(x) = p(−x)}
Find W = P(e) ∩P3. Find a basis for W and find the dimension of W
Show the cartesian product of R^n and R^m, is isomorphic to R^(n+m)
Let V = R3
, A = {(x, y,z)|y = 0} and B = {(x, y,z)|x = y = z}. Check whether
R3 = A⊕B
a.find a basis for the span of the following set of vectors
|1 | |-4 | |1 | |5| |2| | -1| |11|
|3 | |-12| |-4| |8| |11| | -7| | 52 |
|-1| | 4 | |-5| |-17| |-21| |19| | -80|
|2| |-8| |4| |16| |17| | -3| | 82|

b. find the coordinate vector [x]B for the vector(see below) using the basis from a above
|-8|
|-58|
|151|
|-58|
Solve the following
0.6x + 0.8y + 0.1z = 1
1.1 x + 0.4y + 0.3z= 0.2
x + y + 2z =0.5
by LU decomposition method and find the inverse of the coefficient matrix
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