QUESTION 4 (-2 1 -4 2 -1 6 Find the rank and nullity of the matrix A. A= 1 2 -1 10 ) A Rank(A)=1 and Nullity(A)=2. OB. Rank(A)=2 and Nullity(A)=1. oc Rank(A)=3 and Nullity(A)=0. OD. Rank(A) = 0 and Nullity(A)=3.
Math 2890 QZ-6 SP 2018 1) Find the rank of the following matrix. Also find a basis for the row and column spaces. 1 0 3 3 10 0 -1 2 Find a basis of Null(A) where A is the given matrix. Find the rank of A and dimension of Nul(A). Let B be an invertible 4X4 matrix (a matrix with 4 rows and 4 columns). Is the matrix AATB also invertible? Explain.
Find a basis for the row space and the rank of the matrix. -3 -6 6 5 4 -4 -4 2 -3 -6 6 9 (a) a basis for the row space 33} (b) the rank of the matrix 3
The rank of the matrix 4 -8 0 16 6 2 2 0 -2 -10 -2 16 6 16 4. 24 is Select one: O A. 4 O B. 3 O C. 1 O D. 2 O E. None of these answers
a) If A is a 3 x 6 matrix and Rank(A) = 2, then what is the dimension of Nul(A)? b) If B is a 8 x 5 matrix and the dimension of Nul(B) = 3, what is the dimension of Col(B)? c) If C is a 4 x 8 matrix, what is the largest possible dimension of Row(C)?
PLEASE ANSWER ALL PARTS
1. (2 points) For the matrix A=| 3 | 6 | Evaluate (a) A, AA* and AA; (b) the value P (A), where P(x)-x3-1. 2. (1 point) Compute the determinant of the matrix A = | α β 2 -8 6 8 2 -7 7 10 3, (1 point) Compute | 1 -3 0 6 4. (1 point) Find the inverse matrix A-' of the matrix A=1 5 3-2 7 4 -3 5. (3 points) Find...
Q.2. Find the rank of the following matrix 1 2 2 1 2 -2 11 A= -2 -4 3 6 3 k where ‘k’ is any fixed constant.
1. (2 points) Consider a 6 x 4 matrix A, with rank 3. Complete the following (Hint: Figure 4.2): The column space, C(A), is a subspace of R and has dimension r. Its orthogonal complement is the - space, is a subspace of R_, and has dimension —_. The row space, C(AT), is a subspace of R and has dimension r. Its orthogonal complement is the – _space, is a subspace of R_, and has dimension . Hint: Read Strang's...
linear alebra
can you do problems 5&6 please.
5. If A is 2 by 3 and B is 3 by 2 ani AB = 1, show from its rank that BA 1. 3 points 6. Find the LU factorization of the matrix for the matrix A [10 points A=11-1 0 1-14 0 -4 What is the LDU factorization? Find the complete solution of Ar = b with b given above.
5. If A is 2 by 3 and B is...
(a) Why is it impossible for a 3 x 4 matrix A to have rank 4 and dim Nul A = 0? (b) What is the rank of a 6 x 8 matrix whose null space is three-dimensional? (c) If possible, construct a 3 x 5 matrix B such that dim Nul B =3 and rank B = 2. Explain your reasoning. (d) Construct a 4 x 3 matrix C with rank 1. It need not be complicated.