let a₁, a2 and a3 be the columns of A, let B = {a1, a2, a3} and let H = span(B).

Q: Can 2 diagonals in cube ever be mapped on to a single diagonal?  No, why?

A:

Q: find the rank, nullity, row space & null space of the ff: A = [1, 5, 3, 2 0, 4, 2, 1 0, 8, 4, 5 1,…

A:

Q: Find the greatest common divisor (GCD) and the least common multiple (LCM) of 1575 and 66. Hence…

A: Given number's 1575 & 66  Division algorithm: If m and n are integers and n is positive there…

Q: Explain the dimension of the row space.

A: The dimension of the row space is called the rank of the matrix. This is the same as the maximum…

Q: Find minor and cofactor of the first row and then use them to find 3 -7 -1 0 -8 8 2 3 -7 -1 = Choose…

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Q: Is the span of a matrix A is the same as the column space of A? T or F

A: We shall answer this question in next step

Q: Let M,xn be a set of squarenx n-matrices. Is the set Mnxn a vector space? Explain. Find 2 different…

A: We find two different basis of M_2×2

Q: In linear algebra, the column space and the row space have the same dimension.   (True or False)

A: The given statement, "The column space and the row space have the same dimension".The objective is…

Q: What are free columns?

A: A matrix is a rectangular array containing the set of numbers arranged in rows and columns. A matrix…

Q: Find the dimension for M3,2

A:

Q: [61] Diagonalize B = (by finding P and D) or explain why B isn't diagonalizable.

A:

Q: Calculate B(5,2) if B (a,r) = 2ar+r^3

A: I have to calculate B(5,2) It is given that B(a,r) = 2ar+r3

Q: Describe the column space of a reduced row echelon matrix R.

A: Leading 1: When the leftmost entry in a row is 1 and all the entries above and below of the leading…

Q: Find A x B x C where A = {2, 5}., B = {13, 17}, C = {0} . O (2,13,0), (2, 17,0), (5, 13, 0), (5, 17,…

A:

Q: Find the value of x that satisfies the following equation (2x – 5yi) + (y + xi) = 8-7i В. 4 А. 2 С.…

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Q: let a1 is (-3,2,6) a2 is (-9,-7,-2) and b is (-18,-27,-23). Is b in the span of of a1 and a2

A: The objective of this question is to determine whether the vector b is in the span of vectors a1 and…

Q: Find the polynomials connecting the points (0,1), (1,3), and (2,13) ​​by quadratic interpolation.

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Q: Write 2x + 3y + z + 5t = 8 as a matrix A (how many rows?) multiplying the column vector x = (x, y,…

A: Given: Equation is Objective:Represent the equation in matrix form, , where  is the coefficient…

Q: Explain why v = ( 1, 0, -1) cannot be a row of A and also in the nullspace.

A:

Q: Let a,b, and c be distinct real numbers, and * be any real number. Determine if the empty blank…

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Q: Consider the following linear equations: -6x + 3y + 6z -6x + (16-k)y + 5z -6x + 3y + (8 - k)z a) -6…

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Q: 81. What is wrong with the following calculation? 0 =0 +0 + 0 + ... = (1 – 1) + (1 – 1) + (1 – 1) +…

A: Given a calculation.

Q: if (A|b) is in reduced row echelon form, prove that A is also in reduced row echelon form.

A: (A|b) is the augmented matrix formed by placing elements of matrix B to the right of elements of…

Q: stitution? I have to use the Column Correspon

A: Is (1,2,3,4,5,6)∈ span( (1,1,1,1,1,1),(0,1,0,1,0,2),(6,5,4,3,2,1)) > A x1 x2 x3 x4 x5 x6…

Q: Let A be an m x n matrix and let b and c be column vectors with n components. Express the dot…

A: Answer :

Q: Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c), (b,d),(b,e),(d,

A:

Q: Find the dot product: (-1, 0,1) . (1, 9, 2). Fully reduce your answer. (It should be a whole number)

A: To find The dot product of (-1,0,1).(1,9,2)

Q: For the numbers 1, 2, 4, 6, 8 Compute:  SX   SX2   (SX) 2

A: Given data is1, 2, 4, 6, 8

Q: a. Express each column vector of AB as a linear combination of the column vectors of A. b. Express…

A: a. To express each column vector of AB as a linear combination of the column vectors of A, we can…

Q: -3 -3 9. 2 Let A = -3 -6 12 and b = 3 -3 -2 13 -5 Denote the columns of A by a1, a2, a3, and let W =…

A:

Q: Find sub spaces row (A), column (A) and null (A). Find rank 103 A=015

A: first we shall find rank of the matrix then find row space, column space and null space

Q: If BD = p- 7 and BF = 6p - 97, find BF in parallelogram CDEF. D. BF C.

A: Given : CDEF is a parallelgram  The diagonals of a parallelgram are bisected by the point of their…

Q: Suppose the second column of B is all zeros.  What can you say about the second column of AB?

A: If the second column of B is all Zeros, then the second column of AB will also be all Zeros.