Example: Let 4 1 S = Span| ui = 3 ,U4 = , u2 = ,u3 = , U5 = 1 -2 6 6. We find a row-echelon form of the matrix A = [u1 u2 u3 U4 U5]: 1 1 1 4 [1 1 1 4 1 3 7 1 -2 -1 1 -6 1 -2 -2 -4 1 -1 1 0 0 The pivot columns are columns x (enter your answer as a list of numbers in increasing numerical order, separated by commas but no spaces), so a basis for S is

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A: The first step in solving a system of linear equations is to write the system as an augmented…

Q: 4 1 34. The rank of the matrix A = 2 -1 is -7 -14 4 8 -1 (A) 1 (B) 2 (C) 3 (D) 0 (E) 4

A: To find The rank of a given matrix A.

Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

A: Given that,  v=3,6,6,-3,1u1=1,1,-1,2,1u2=2,1,2,-1,1u3=1,2,0,1,2u4=0,2,0,1,-4u5=1,1,2,-1,2 Find the…

Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

A: Let u1,u2,…,un be a set of vectors in the vector space V and v be any vector in V. The vector v can…

Q: Use part (iii) of the rank of a matrix by row reduction theorem to find the rank of the given…

A: Sol:- 1-22-45135Reduce matrix to reduced row echelon form 1  ⋯  b 0 ⋱  ⋮0  0  1Swap matrix rows: R1…

Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

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Q: 2 1 -1 3 1 9. Calculate the rank of the matrix P = | 2 1 2 0 3 1 1 1 |-1 -5 -3 -7 3|

A: P=210-131212003111-1-5-3-73

Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

A: Maxima program used to solve:

Q: kpression for "12 times x."

A: Times means multiplication. Sometimes it is denoted by dot.

Q: Carry out row operations to reduce th matrix upper triangular form 2 -1 4 4 -1 -6 8 -2 3.

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Q: -8 a 3 0-2 is the minor of matrix A = 2 -5 Given M = 4 -4 6. 4 %3D 16 -15 1 2 -2 Determine the…

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Q: Find the row reduced echelon  matrix R and invertible matrix P such : R = PA             -1     1…

A: The given matrix is: A=-11-10-34114-6-4-2310-14. To find row reduced echelon form of given matrix,…

Q: Find the rank of the matrix A = rank(A) = 3 0 12 -4 -5 1 -3 -23 -16

A: We have a Matrix A and we have to calculate rank of it.Concept: Since A is square Matrix. If det(A)…

Q: Reduce the matrix A below to Row Echelon Form (REF) 0 1 0 -4 3 -1 -1 3 4 0 0 0 3. A =

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Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

A: We have to write the vector v=3, 6, 6, -3, 1 as the linear combination of the vectors u1, u2, u3, u4…

Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

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Q: [2 Given that; a=1, b=2, c=0, d=1 Explain why the matrix a b c d is not diagonalisable.

A: Here the given matrix Let x be tha eigen value of A matrix Then

Q: 1 3 3 1 3 -2 2 -1 -1 -1 0 -4 1 1 1 -5 A = B = 2 -8 1 2 -3 7 - 3 -1 -2 -8 2 -1 20. Can every vector…

A: As we know basis of the column space of matrix B is formed by columns of B that correspond to the…

Q: Suppose A is a 4 x 8 matrix with 5 pivots. What can be said about the dimension of the column space…

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Q: Express the column matrix b as a linear combination of the columns of A. (Use A₁, A2, and A3…

A: The given matrix and a vector, and .The objective is to write the vector  as a linear combination of…

Q: Let A be a 5 x 4 matrix and b a nonzero vector in R5. We are told the system Ar = b has infinitely…

A: Given A be a 5 x 4 matrix and b a nonzero vector in R5 That is, there are 4 equations and  unknown…

Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

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Q: Solve the initial value problem below using the method of Laplace transforms. - 4t y" - 16y = 16t –…

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