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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).

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

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

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

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

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

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 = {(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|

|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

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