Question

Reduce the given matrix into normal form & find its rank​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

The rank of the matrix A is 3

Step-by-step explanation:

The given matrix is

$A=\left[\begin{array}{ccc}3&-4&21\\-6&3&9\\4&-3&1\end{array}\right]$

First, reduce the matrix into the upper triangular matrix by using the elementary row operations.

R1 → R1/3

$A=\left[\begin{array}{ccc}1&\frac{-4}{3} &7\\-6&3&9\\4&-3&1\end{array}\right]$

R2 → R2 + 6R1

R3 → R3 - 4R1

$A=\left[\begin{array}{ccc}1&\frac{-4}{3} &7\\0&-5&51\\0&\frac{7}{3} &-27\end{array}\right]$

R2 → R2/-5

$A=\left[\begin{array}{ccc}1&\frac{-4}{3} &7\\0&1&-10.2\\0&\frac{7}{3} &-27\end{array}\right]$

R3 → R3 - (7/3)R2

$A=\left[\begin{array}{ccc}1&\frac{-4}{3} &7\\0&1&-10.2\\0&0&-3.2\end{array}\right]$

R3 → R3/-3.2

$A=\left[\begin{array}{ccc}1&\frac{-4}{3} &7\\0&1&-10.2\\0&0&1\end{array}\right]$

Since there are 3 non-zero rows, the rank of the matrix is 3

Rank(A) = 3