Find the general solution for the system of equations using parameters as needed: r, s, t: x+y+2z=5 x+z=-2 2x+y+3z=3 Use of technology is okay, but must be documented carefully. All steps must be recorded except for the calculations, including any rewrite to matrix form. Include in your work the input to the technology, the command for the tech, document what technology you used, show the output. Be sure to answer the question (do not leave the "interpretation" of the output to your reader) a. Show the solution to the given system as a linear combination of column vectors using your chosen parameters. b. Give a basis for the solution space for
Find the general solution for the system of equations using parameters as needed: r, s, t:
x+y+2z=5
x+z=-2
2x+y+3z=3
Use of technology is okay, but must be documented carefully. All steps must be recorded except for the calculations, including any rewrite to matrix form. Include in your work the input to the technology, the command for the tech, document what technology you used, show the output. Be sure to answer the question (do not leave the "interpretation" of the output to your reader)
a. Show the solution to the given system as a linear combination of column vectors using your chosen parameters.
b. Give a basis for the solution space for the corresponding homogeneous system of equations. (You have been given the equivalent of Ax=b, find the basis for solution of Ax=0 written as a set of column vectors based on your answer to part (a)).
c. Give the dimension of the homogeneous solution space.
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