Recent questions tagged matrix

Let $A=\begin{pmatrix} 1 & 1 & 0\\ 0 & a & b\\1 & 0 & 1 \end{pmatrix}$. Then $A^{-1}$ does not exist if $(a,b)$ is equal to$(1,-1)$$(1,0)$$(-1,-1)$$(0,1)$

$1)$ How to find a matrix is diagonalizable or not?Suppose a matrix is $A=\begin{bmatrix} \cos \Theta &\sin \Theta \\ \sin\Theta & -\cos\Theta \end{bmatrix}$Is it diagona...

Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alp...

The rank of the matrix $\begin{bmatrix} 0 &1 &t \\ 2& t & -1\\ 2& 2 & 0 \end{bmatrix}$ equals $3$ for any real number $t$$2$ for any real number $t$$2$ or $3$ depending o...

Let $A$ be a $3 \times 3$ real matrix. Suppose 1 and -1 are two of the three Eigen values of $A$ and 18 is one of the Eigen values of $A^2+3 A$. ThenBoth $A$ and $A^2+3 A...

how to prove determinant 1 and 2 are same by some row-column manipulation ,please Help??

Consider the set H of all 3 × 3 matrices of the type:$\begin{bmatrix} a&f&e\\ 0&b&d\\ 0&0&c\\ \end{bmatrix}$where a, b, c, d, e and f are real numbers and $abc ≠ 0$. Unde...

Which homogeneous $2D$ matrix transforms the figure (a) on the left side to figure (b) on the right? $\begin{pmatrix} 0 & 2 & -6 \\ 2 & 0 & 1 \\ 0 & 0 & 1 \end{pmatrix}$$...

$\begin{bmatrix} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{bmatrix}$For the above given matrix $A,$$A^3 -7A^2 +10A = $$5I+A$$5I-A$$A-5I$$6I$

Consider the matrix$$A = \begin{bmatrix} \frac{1}{2} &\frac{1}{2} & 0\\ 0& \frac{3}{4} & \frac{1}{4}\\ 0& \frac{1}{4} & \frac{3}{4} \end{bmatrix}$$What is $\displaystyle ...

The value of $p$ such that the vector $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is an eigen vector of the matrix $\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10...

If $C$ is a non-singular matrix and $B=C \begin{bmatrix} 0 & x & y \\ 0 & 0 & x \\ 0 & 0 & 0 \end{bmatrix} C^{-1}$ then:$B^2=I$$B^2 = \text{Null Matrix}$$B^3=I$$B^3 = \te...

I had already visited below link but was unable to grasp it.https://math.stackexchange.com/questions/218770/when-does-a-square-matrix-have-an-lu-decomposition.I made some...

IF A=$\begin{bmatrix} 2& -0.1\\ 0 & 3 \end{bmatrix}$ AND A-1=$\begin{bmatrix} \frac{1}{2}& a\\ 0 & b\end{bmatrix}$ then a+b ?a)$\frac{7}{20}$ b)$\frac{3}...