[2 4 -1 2] Let A = 0 3 2 1. Then the dimensions of the row space, column space, 12 4 2 ol and nullspace of A are, respectively: a) 3,2,0. b) 3,3,1. c) 2,2,1. d) 2,3,0.

Q: Determine whether w is in the column space of A, the null space of A, or both. 1 - 8 5 -2 0 - 5 2 1…

A: W belongs to only null space of A.

Q: If A is diagonalizable and B is diagonalizable, must it be true that AB is diagonalizable? Give a…

A: If A is diagonalizable and B is diagonalizable then it is not necessary for AB to be diagonalizable.…

Q: In Exercises 9-10, find bases for the null space and row space of A. 1 -1 3 | * 9. (a) A =5 -4 -4…

A:

Q: 2 If A is diagonalizable then A is diagonalizable. Select one: O True False

A:

Q: In Exercises 9–10, find bases s for the null space and row space of 2. b. А —D | 4 -1 3 -1] 9. а. А…

A: Here in this question we need to find out the basis for null space and row space of the given…

Q: 2. Prove that: k(4+ mB) - kA+(km) B for any mx n matrices A and B, and scalars k and m. (You may not…

A: 2 We have to prove that kA+mB=kA+kmB Where, A and B are m×n matrices and k and m are the scalars.…

Q: If the column space of a 3x3 matrix consists of all vectors b=[b1 b2 b3] such that b1+ b2= 3b3 then…

A:

Q: The set of all polynomids of degree 4 under the standard addition and scalar multiplication…

A: Addition of polynomials

Q: Find bases of for the column space of A, row space of A, and the null space of A 1 1 -1 0 2 -2 A = 2…

A:

Q: 1 00 0 2 <-5 0 21. 0 0 0 4 22. -3 -4 -3 4 0 0 0 1 -2 1 3 0 3 8 -5, In Exercises 23-24, find the…

A:

Q: 2. Find bases for i) the row space, ii) the column space, and iii) the null space of the matrix 3 -3…

A: The given problem is to find the bases of row space , column space , null space of the given matrix.

Q: Prove using elements that for any square matrices A,B of the same size and constant K.…

A: For any square matrices A,B of the same size and constant K.  tr(kA+B)=ktr(A)+tr(B)

Q: 6. A Latin square L is self orthogonal if L and its transpose L' are orthogonal. 6.1. Show that a…

A: The elements of a Latin square are taken from a field. It is a square arrangement in which each…

Q: Find the orthogonal complement of the null space of A. 1 -2 (a) A =| 2 2 2 4 -1 6. 1. -1 3 2 (b) A =…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Is the set of polynomials {-1+ 3t – 21², 4 – 10t + 312, 4 – 8t – 212} independent? Answer this…

A:

Q: Compute the product AB by the definition of the product of matnices, where Ab, and Ab, are computed…

A: . ...................setup .................final answer

Q: It can be shown that Ax=b where b= (8,4, – 8) = (8, - 2) is a least squares solution of and A =…

A:

Q: Enter the missing coefficients for the row operations. 1 0 (1) O R, - R;: 0 3 1 15 5 2 -4 28 1 0 O…

A:

Q: (3' 2 5 1 1. Determine whether v =2 is in the column space or null space ofA = -1 -7 -5 5. 3 4 -2/

A: Note -  Acc. to Bartelby guidelines , we are supposed to do only one question . If you want more to…

Q: State Cayley-Hamilton theorem and prove this for following matrix [1 1 A 1 2 -1 %3D [5 8

A:

Q: 3. Consider the following linear system: AZ =7, %3D where 1 1 1 - 1 and (a) What is the dimension of…

A: To find the rank and dimension of column space of matrix put the matrix into reduced row echelon…

Q: Find bases for the colume space the row space and the 3 A- 6 15 1 column space of A- -YAR

A:

Q: Consider the system Ax = b where A = and b = {[;} basis for the null space of A is given by and ox s…

A: Consider the system Ax = b   To determine the row spa Determine c value and substitute then get row…

Q: linear algebra question.

A:

Q: 5. Let a b M22 | а, b, с, d € R с d Show that M22 with the usual matrix addition and scalar…

A:

Q: Assume that th e product AB makes sense Prove that if the columns of B are linearly dependent, then…

A:

Q: Find the dimension of the null space and the dimension of the column space of the -3 -2 7 7 [1 -27 2…

A: The given matrix, M=1-3-277-22-6-45147 we have to find dim(Nul(M)) and dim(col(M))

Q: 13. Find all 2 x 2 matrices A = (" ta² = (C :) such that %3D

A: We need to find the set of all 2×2 matrices such that A2=O, where O is the zero matrix of order 2.

Q: Prove as follows the inequality |Ax| =||A|| - |x|, where A is an m x m matrix with row vectors a1,…

A: Given: The order of the matrix A is m×m. The row vectors are a1,a2,a3,.....am and the dimensional…

Q: Compute the products in Exercises 1–4 using (a) the definition, as in Example 1, and (b) the…

A: Let the given matrices be A and B,A = -421601B = 3-27 Order of matrix A = 3×2Order of matrix B =…

Q: such that the vector 2 is a solution of 13. Construct a 3 x 3 nonzero matrix Ax = 0 123

A: I have construct a block matrix

Q: of the null space and the dimension of the column space of the -6 8 12 3 -47 2 12 4 -6 6 -8 (a)…

A: We know that  rank(M) = dim( Col(M))

Q: 4 Let W be the set of all vectors of the form -(4r +3s + t) | 2r – 3s +t 4r + 2s – 2t (3r + 2s + 5t)…

A:

Q: (a) Suppose addition in R? adds an extra 1 to each component, so that (3, 1) + (5,0) = (9,2) in-…

A: As per our guide lines we can only answer one question and you would have to repost the other…

Q: In exercises 8 to 13 , explain how your calculations justify your answer, and mention an appropriate…

A:

Q: / Find a Row A, CoL A, Null (A), whore. A= bazis and dimension Lor 2. 1- -31 -2

A: we have to solve given problem:

Q: Matrix B was obtained by row reducing A. 2. 5 - 5 5 21 3 7 18 – 19 17 76 11 A = 4 8 -4 12 32 4 1 0 5…

A:

Q: The columns of AB are combinations of the columns of A. This means: The column space of AB is…

A:

Q: Show that if M, - M. - (C ). (6 ). Ms - (: :). M2 = %3D %3D then the span of {M1, M2, M3} is the set…

A:

Q: Show that a. A is diagonalizable if (a – d)² + 4bc > 0. b. A is not diagonalizable if (a – d)² + 4bc…

A:

Q: Let M be a real square matrix such that M3 + M = 2M². Prove that M is diagonalisable.

A:

Q: The set of 2 x 2 matrices Mgxa with standard matrix operations is a vector space. Problem In Mara…

A:

Q: Find the dimension of the null space and the dimension of the column space of the 1 -3 -2 7 7 -2…

A:

Q: .. Find A basis for the nullspace and column space of 1 2 1 1 2 2 2 4 3 2 1 1 2 A = 3 3 1 -1 -1 |

A:

Q: While trying to invert A, [A I] is carried to [P Q] by row operations. Show that P=QA.

A: [A I] is carried to [P Q] by row operations. So, A is carried to P and I is carried to Q. Since A is…

Q: ve bases for row(A), col(A), and null(A): -- 1 1 A = 0 1 -1 0 1 -1 -1 w(A):

A:

Q: 5.2.7 Show that Ae³A™ = eABA' for any orthogonal matrix A.

A: To show: AeBAT=eABAT for any orthogonal matrix A.

Q: If the column space of a 3x3 matrix consists of all vectors b=[bj b2 b3] such that b,+ b2= 3b3 then…

A: The column space of a 3×3 matrix consists of all vectors b=b1 b2 b3 such that b1+b2=3b3 then one of…

Q: Find the dimensions of the null space and the column space of the given matrix. 1 5 130 -2 -4 -5 -4…

A: We need to determine he dimensions of the null space and the column space of the matrix: 15130…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.