Math  /  Algebra

QuestionOfficial Time: 15:10:03
Question 1 [10 points] Consider the following matrix AA : A=[51010121354366]A=\left[\begin{array}{ccc} 5 & -10 & 10 \\ -1 & 2 & 1 \\ 3 & -5 & 4 \\ -3 & 6 & -6 \end{array}\right]
For each of the following vectors, determine whether the vector is in the image of AA. If so, demonstrate this by providing a vector x\mathbf{x} so that Ax=biA \mathbf{x}=\mathbf{b}_{\mathbf{i}}. b1=[2041112]b1 is in im(a): A[000]=b1\mathbf{b}_{1}=\left[\begin{array}{c} 20 \\ -4 \\ 11 \\ -12 \end{array}\right] \quad \begin{array}{c} \mathbf{b}_{1} \text { is in im(a): } \\ A\left[\begin{array}{l} 0 \\ 0 \\ 0 \end{array}\right]=\mathbf{b}_{1} \end{array} b2=[5433]b2 is in im (a):b3=[000]=b2b3=[91066]b3 is in im (a):[000]=b3\begin{array}{l} \mathbf{b}_{2}=\left[\begin{array}{c} -5 \\ 4 \\ -3 \\ 3 \end{array}\right] \quad \begin{array}{c} b_{2} \text { is in im }(a): \\ b_{3}=\left[\begin{array}{l} 0 \\ 0 \\ 0 \end{array}\right]=b_{2} \\ b_{3}=\left[\begin{array}{c} 9 \\ -10 \\ 6 \\ -6 \end{array}\right] \\ b_{3} \text { is in im }(a): \\ {\left[\begin{array}{l} 0 \\ 0 \\ 0 \end{array}\right]=b_{3}} \end{array} \end{array} SUBMIT AND MARK SAVE AND GLOSE

Studdy Solution
None of the vectors b1\mathbf{b}_1, b2\mathbf{b}_2, or b3\mathbf{b}_3 are in the image of AA.

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