1)false , this is not closed under addition or scaler multiplication .
as if we take x2+x3 , where x2 and x3 are reals so , their sum does not contained in W and for any scaler a , a.x2 does not belong to W so , not closed under both operation .
2)true, this is defination of basis.
3)false , the n * n identirty matrix is invertible , but the row vectors are linaerly independent .
when matrix is invertible it is row equivalent to identity matrix , so like identily matrix of order n*n , our matrix also have n pivots hence , rows are said to be linearly independent .
DETAILS LARLINALG8 4.R.084. ASK YOUR TEACHER Determine whether each statement is true or false. If a...
12. [-13.22 Points] DETAILS LARLINALG8 3.2.038. ASK YOUR TEACHER Determine whether ebch statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. (a) Adding a multiple of one column of a square matrix to another column changes only the sign of the determinant....
Determine whether each statement is True or False. Justify each answer. a. A vector is any element of a vector space. Is this statement true or false? O A. True by the definition of a vector space O B. False; not all vectors are elements of a vector space. O C. False; a vector space is any element of a vector. b. If u is a vector in a vector space V, then (-1) is the same as the negative...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
the last pic is number 14 please answer it as a,b,c,d as
well.
thanks
1. If A is diagonalizable then A is diagonalizable. a) True b) The statement is incomplete c) False d) None of the above 2. In every vector space the vector (-1)u is equal to? a) -U b) All of the above c) None of the above d) u 3. The set of vectors {} is linearly dependent for a) k = 3 b) k = 1...
14) V is a vector space. Mark each statement True or False. a. The number of pivot columns of a matrix equals the dimension of its column space. b. A plane in R' is a two-dimensional subspace of R'. c. The dimension of the vector space P, is 4. d. If dim V = n and S is a linearly independent set in V. then S is a basis for V. e. If a set fv.....v} spans a finite-dimensional vector...
(a) State whether the following statement is true or false. The follow set is a subspace of P2, where P2 is the set of all polynomials over the real numbers of degree 2 or less. W={p € P2 :p (3)=0} O True O Fale In the essay box below, if it is true, prove that W is closed under scalar multiplication. Otherwise, give an explantion why the statement is false. XDX HE Editor A-AIBIU S *** Styles Font Size Words:...
DETAILS LARLINALG8 4.R.023. Determine whether W is a subspace of the vector space V. (Select all that apply.) W = {f: f(0) = -1}, V = C[-1, 1] W is a subspace of V. W is not a subspace of V because it is not closed under addition. W is not a subspace of V because it is not closed under scalar multiplication.
Decide whether each statement is true or false and explain your reasoning. Give a counter-example for false statements. The matrices A and B are n x n. a. The equation Ax b must have at least one solution for all b e R". b. IfAx-0 has only the trivial solution, then A is row equivalent to the n x p, identity matrix. c. If A is invertible, then the columns of A-1 are linearly independent. d. If A is invertible,...
Can
you please answer questions 1-6,thank you a lot!Thumbs up for great
answer,Thx!
Remember: to show that a property is true you must check every possibility (probably using variables and general vectors). To show that a property is false you only need to give one counterexample. 1. Find a set of vectors in R2 which is closed under vector addition but not scalar multiplication. 2. Find a set of vectors in R? which is closed under scalar multiplication but not...
[-/1 Points] DETAILS LARLINALG8 4.3.003. Is W a subspace of V? If not, state why. Assume that has the standard operations. (Select all that apply.) W is the set of all 2 x 2 matrices of the form [1] V = M2,2 W is a subspace of V. W is not a subspace of because it is not closed under addition. W is not a subspace of V because it is not closed under scalar multiplication. Submit Answer Viewing Saved...