I need to calculate the rank of the matrix A,

ahgan3j 2021-11-22 Answered
I need to calculate the rank of the matrix A, shown below:
\[\begin{bmatrix}3 & 2 & -1\\2 & -3 & -5\\-1 &-4 &-3 \end{bmatrix}\]

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Expert Answer

George Spencer
Answered 2021-11-23 Author has 1656 answers

Simply use row reduction: the rank is the number of non-zero rows after you've performed row reduction:
\(\begin{bmatrix}3 & 2 & -1\\2 & -3 & -5\\-1 &-4 &-3 \end{bmatrix}\rightsquigarrow\begin{bmatrix}1 & 4 & 3\\3 & 2 & -1\\2 &-3 &-5 \end{bmatrix}\rightsquigarrow\begin{bmatrix}1 & 4 & 3\\0 & -10 & -10\\0 &-11 &-11 \end{bmatrix}\rightarrow\begin{bmatrix}1 & 4 & 3\\0 & 1 & 1\\0 &-11 &-11 \end{bmatrix}\rightsquigarrow\begin{bmatrix}1 & 4 & 3\\0 & 1 & 1\\ 0 &0 &0 \end{bmatrix}\)

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Ourst1977
Answered 2021-11-24 Author has 458 answers
I am looking for a solution myself, I will be grateful for help with the solution
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