The row echelon form of matrix A is given by: 1 -5 31 0 1 Lo o o 0 [1 3 4 Then a basis for the row space of A is: {(1,0,0); (1,1,0)} {(1,2,1, -5,3); (0,0,1,3,4), (0,0,0,0,0)}, None of these O {(1,2,1, -5,3); (0,0,1,3,4)}

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A: Using Langrage multiplier:  ∂∂x,∂∂y,∂∂zx2+y2+z2=λ∂∂x,∂∂y,∂∂zlx+my+nz 2x=λl2y=λm2z=λn x=λ2ly=λ2mz=λ2n

Q: 2. The matrix product G o) ( (5 3 is equal to 3 2 5 3 (: ) 3 5

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Q: 2 2 1 6 4 4 1 10 88 8 -1 4 13 26 23

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Q: (v) 0 -1 0 1 0 0 ma ~ 0 ( 1 a -1 0 0 0 a 0 0 a 1 0 1 000

A: Given: A matrix .To find: The Row operations by which the matrix is reduced to

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A: See answer below

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A: I have explained everything with in the solution. Please go through that.

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A: As per our guidelines I am solving only first matrix please resubmit other matrices

Q: 1. Consider the matrices 0 4₁-(13), 1 3)₁ 4₂2 - ( -8 -2) ₁4₁ = (3-2). 0 1 3 -5 -4 A₁-(3) -4 0 and A4…

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A: Let (a,b,c) be any element of R3, then (a,b,c)=(x,y,0)+(0,y,z)=(x,2y,z) ⇒a=x, b=2y, c=z ⇒a,b,c∈R ⇒…