(a) Find the rank of the following matrix $A$ for various values of $…

Question

(a) Find the rank of the following matrix $A$ for various values of $k$

$$A = \begin{bmatrix} 1 & k & -1 & 2 \\ 2 & -1 & k & 5 \\ 1 & 10 & -6 & 1 \end{bmatrix}$$

(b) Find the eigen values and their corresponding eigen vectors for the matrix

$$\begin{bmatrix} 8 & -8 & -2 \\ 4 & -3 & -2 \\ 3 & -4 & 1 \end{bmatrix}$$

(c) Using Cayley Hamilton Theorem, find the inverse of the matrix

$$\begin{bmatrix} 1 & -1 & 1 \\ 4 & 1 & 0 \\ 8 & 1 & 1 \end{bmatrix}$$

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More PYQs on Rank of a Matrix

• (a) Find the rank of the following matrix A for various values of k $$A = \begin{bmatrix} 1 & k & -1 & 2 \\ 2 & -1 & -k & 5 \\ 1 & 10 & -6 & 1 \end{bmatrix}$$…