Question content area top part 1 let u 9112 and a 5 8 12 1 2...

Question content area top Part 1 Let u = [9;1;12] and A = [ 5 8 12; 1 2 2; 3 2 10] . Is u in the subset of spanned by the columns of A? Why or why not? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal for each matrix element.) A. No, the reduced echelon form of the augmented matrix is enter your response here, which is an inconsistent system. B. Yes, multiplying A by the vector enter your response here writes u as a linear combination of the columns of

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00:01 In this question, we are given the vector u and the matrix a.

00:06 And we are asked to determine if u is in the space spanned by the columns of the matrix a, which is also called the column space of a and denoted by call a.

00:20 It's basically all possible sums of the columns of the matrix a, that's all.

00:27 In other words, we are asked to determine if the equation a x equals to u has solutions.

00:39 So we are trying to solve the equation a x equals you.

00:42 The augmented matrix of the system is going to be 8, 5, 8, 12, negative 7, 0 ,1, negative 1, negative 4 in the second row, and 1, 2, 2, negative 2, negative.

01:01 1 in the third row.

01:07 Now we want to reduce this matrix to a row echelon for.

01:12 The first step would be to interchange the first and the last rows.

01:18 Now the last row becomes the first row.

01:22 1 -2 -2 -1.

01:26 The second row is going to be same.

01:29 0 -1 -9 -4.

01:35 And the first row becomes the last row.

01:38 5 -8 -12 -negative -7.

01:50 Now we will use the first pivot to get rid of the 5 underneath it.

01:57 So we need to multiply the first row by negative 5 and add it to the last row...