Question

True or False? (Make sure to justify your answer.) For this question let ?A be a...

True or False? (Make sure to justify your answer.)

For this question let ?A be a non-zero ?×?m×n matrix, and ?B an invertible ?×?n×n matrix.

If {?1,...,??}{x1,...,xk} is a basis for null(?)null(A), then dim(null(??))=?dim(null(AB))=k.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Indicate whether each statement is True or False. Briefly justify your answers. Please answer all of...
Indicate whether each statement is True or False. Briefly justify your answers. Please answer all of questions briefly (a) In a vector space, if c⊙⃗u =⃗0, then c= 0. (b) Suppose that A and B are square matrices and that AB is a non-zero diagonal matrix. Then A is non-singular. (c) The set of all 3 × 3 matrices A with zero trace (T r(A) = 0) is a vector space under the usual matrix operations of addition and scalar...
True or false; for each of the statements below, state whether they are true or false....
True or false; for each of the statements below, state whether they are true or false. If false, give an explanation or example that illustrates why it's false. (a) The matrix A = [1 0] is not invertible.                               [1 -2] (b) Let B be a matrix. The rowspaces row (B), row (REF(B)) and row (RREF(B)) are all equivalent. (c) Let C be a 5 x 7 matrix with nullity 3. The rank of C is 2. (d) Let D...
Answer all of the questions true or false: 1. a) If one row in an echelon...
Answer all of the questions true or false: 1. a) If one row in an echelon form for an augmented matrix is [0 0 5 0 0] b) A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax=b has at least one solution. c) The solution set of b is the set of all vectors of the form u = + p + vh where vh is any solution...
True or False (5). Suppose the matrix A and B are both invertible, then (A +...
True or False (5). Suppose the matrix A and B are both invertible, then (A + B)−1 = A−1 + B−1 . (6). The linear system ATAx = ATb is always consistent for any A ∈ Rm×n, b ∈Rm . (7). For any matrix A ∈Rm×n , it satisfies dim(Nul(A)) = n−rank(A). (8). The two linear systems Ax = 0 and ATAx = 0 have the same solution set. (9). Suppose Q ∈Rn×n is an orthogonal matrix, then the row...
True or False? No reasons needed. (e) Suppose β and γ are bases of F n...
True or False? No reasons needed. (e) Suppose β and γ are bases of F n and F m, respectively. Every m × n matrix A is equal to [T] γ β for some linear transformation T: F n → F m. (f) Recall that P(R) is the vector space of all polynomials with coefficients in R. If a linear transformation T: P(R) → P(R) is one-to-one, then T is also onto. (g) The vector spaces R 5 and P4(R)...
True or False? Justify your answer. If the kernel of matrix A contains two different vectors,...
True or False? Justify your answer. If the kernel of matrix A contains two different vectors, then homogeneous system A.x=θ has infinitely many solutions.
True or false justify your answer 1-The higher the price of X1 the flatter the B.L...
True or false justify your answer 1-The higher the price of X1 the flatter the B.L would be 2-Consumer equilibrium requires that indifference curve intersects the B.L 3-If B.L slope =zero, then a consumer can have an extra unit of good X without paying additional money 4-Cash subsidy is preferred to gift certificate from the store owner view point
This is a TRUE-FALSE Question with justification. If Q is an orthogonal n×n matrix, then Row(Q)...
This is a TRUE-FALSE Question with justification. If Q is an orthogonal n×n matrix, then Row(Q) = Col(Q). The Answer to this is TRUE. I want to know a solid reasoning/explanation for it. In one of the answers, it says that " Since Q is orthogonal, QTQ = I, so Q is invertible, hence Row(Q) = Col(Q) = Rn. But my question is: Why is it that for an invertible matrix, Row(Q) = Col (Q) ? Any other explanation that...
True False questions. Make sure you EXPLAIN EACH ANSWER. 2.19) Suppose that W is a four-dimensional...
True False questions. Make sure you EXPLAIN EACH ANSWER. 2.19) Suppose that W is a four-dimensional subspace of R7 that is spanned by {X1,X2,X3,X4}. Then one of the Xi must be a linear combination of the others. 2.20)Suppose that A is a 3 x 5 matrix such that the vectors X = [1,1,1,1,1]^t, Y= [0,1,1,1,1]^t, and Z = [0,0,1,1,1]^t belong to the nullspace of A. 2.20a) The rows of A are dependent. 2.20b) AX= B has a solution for all...
True or false. If your answer is false, you must justify your answer with a one...
True or false. If your answer is false, you must justify your answer with a one sentence explanation to receive any credit. An asset depreciated in the 3-years MACRS class will have book value of 0 at the end of 3 years. The discounted payback period will always be no shorter than the undiscounted payback period. If the internal rate of return on an investment is positive, then the investment’s net present value must be positive. You are purchasing a...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT