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Q. Find the dimension of the subspace of R4 that is span of the vectors

(█(1¦(-1)@0@1)), (█(2¦1@1@1)),(█(0¦0@0@0)),(█(1¦1@-2@-5))

(█(1¦(-1)@0@1)), (█(2¦1@1@1)),(█(0¦0@0@0)),(█(1¦1@-2@-5))

|2 3 7 |

If |1 x -2 | = 5, find x.

|0 2 x |

If |1 x -2 | = 5, find x.

|0 2 x |

(█(1¦(-1)@0@1)), (█(2¦1@1@1)),(█(0¦0@0@0)),(█(1¦1@-2@-5))

Choose the correct answer.

Q. If the characteristic equation for a 5×5 matrix A is

2λ^5+5λ^4-3λ^2-

Q. If the characteristic equation for a 5×5 matrix A is

2λ^5+5λ^4-3λ^2-

Choose the correct answer.

Q. If F is a linear transformation from R2 to R and F(1,1)=2, F(1,0)=3, then F(2,3)=?

a. 3

b. 2

c. 1

d. -4

Q. If F is a linear transformation from R2 to R and F(1,1)=2, F(1,0)=3, then F(2,3)=?

a. 3

b. 2

c. 1

d. -4

Choose the correct answer.

Q. Let A be an m×n matrix, then which of the following is true.

a. Rank(A)≤m, Nulity(A)≥n

b. Rank(A)≤min(m,n), Nulity(A)≥n-min(m,n)

c. Rank(A)≤m, Nulity(A)≥n-max(m,n)

d. Rank(A)≤m, Nulity(A) ≤n-max(m,n )

Q. Let A be an m×n matrix, then which of the following is true.

a. Rank(A)≤m, Nulity(A)≥n

b. Rank(A)≤min(m,n), Nulity(A)≥n-min(m,n)

c. Rank(A)≤m, Nulity(A)≥n-max(m,n)

d. Rank(A)≤m, Nulity(A) ≤n-max(m,n )

Choose the correct answer.

Q.If M and N are 3 dimensional subspaces of R^6, then what is possible dimension of subspace M∩N?

a. 2,3,4,6

b. 1,2,3,4

c. 0,1,2,3

d. 3,4,5,6

Q.If M and N are 3 dimensional subspaces of R^6, then what is possible dimension of subspace M∩N?

a. 2,3,4,6

b. 1,2,3,4

c. 0,1,2,3

d. 3,4,5,6

Reduce the following equation to standard form hence identify the conic it represents x2 - 3xy + y2 + 4x - 4y - 5 = 0

The form x2 + y2 + z2 and x2 - y2 - z2 are equivalent. True or false

R is a vector space over C with respect to the usual operation of addition and multiplication. true or false.