Find the dimension of the subspace U = span{[1, 1, 1], [2, 5, 2], [1, 2, 3]}.Select one:a. 1b. none of the other choices is truec. 3d. 2

Question

Find the dimension of the subspace U = span{[1, 1, 1], [2, 5, 2], [1, 2, 3]}.Select one:a. 1b. none of the other choices is truec. 3d. 2
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Solution 1

To find the dimension of the subspace U, we need to find the rank of the matrix formed by the given vectors. The vectors are [1, 1, 1], [2, 5, 2], and [1, 2, 3]. We form a matrix with these vectors as rows:

1 1 1 2 5 2 1 2 3

We can simplify this matrix using Gaussian elimination:

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