Problem 4 this is yet another review problem use the

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Problem 4. (This is yet another review problem.) Use the Gram-Schmidt Process to construct an orthonormal basis for R 4 starting with the fol- lowing set of vectors.
Problem 5. (This is also a review problem.) Consider the following matrix: A = 1 2 3 4 0 1 5 7 0 0 1 6 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 (a) View this matrix as a linear transformation between two vector spaces. Identify the domain and the range space (codomain) of this linear transformation. (b) Identify the image of this linear transformation. (c) Write a basis for the image of this linear transformation. (d) Identify the kernel of this linear transformation. (e) Write a basis for the kernel of this linear transformation. (f) What is the column space of this linear transformation? (g) What is the row space of this linear transformation? (h) What is the rank of the matrix A? Problem 6. Convert the following binary numbers to decimal: (a) 11111 (b) 1000000 (c) 1001101101 (d) 10101010 (e) 000011110000 And then, convert the following decimal numbers to binary: (f) 73 (g) 127 (h) 402 (i) 512 (j) 1000 3

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