diagonalizable concept

$1)$ 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...

srestha

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srestha asked May 27, 2019

Linear Algebra
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linear-algebra
matrix

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6 votes

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GO Classes asked Apr 3

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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 1
Let $A$ be an $n \times n$ matrix of real or complex numbers. Which of the following statements are equivalent to: “the matrix $A$ is invertible”? The columns of $A$ are linearly independent. The rows of $A$ are linearly independent. The only solution of the homogeneous equations $Ax = 0$ is $x = 0$. The rank of $A$ is $n$.

Let $A$ be an $n \times n$ matrix of real or complex numbers. Which of the following statements are equivalent to: “the matrix $A$ is invertible”?The columns of $A$ a...

GO Classes

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GO Classes asked Apr 3

Linear Algebra
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linear-algebra
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7 votes

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GO Classes asked Apr 3

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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 2
Let $M$ be a $2 \times 2$ matrix with the property that the sum of each of the rows and also the sum of each of the columns is the same constant $c$. Which (if any) any of the vectors must be an eigenvector of $M$ ... $W = \left[\begin{array}{l}1 \\ 1 \\ \end{array}\right]$ $U$ $V$ $W$ None of the above

Let $M$ be a $2 \times 2$ matrix with the property that the sum of each of the rowsand also the sum of each of the columns is the same constant $c$. Which (if any) any of...

GO Classes

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GO Classes asked Apr 3

Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
eigen-value
easy
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3 votes

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GO Classes asked Apr 3

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GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 3
Let the $n \times n$ matrix $A$ have an eigenvalue $\lambda$ with corresponding eigenvector $v$. Which of the following statements are true for matrix $A$. $-v$ is an eigenvector of $-A$ with eigenvalue $- \lambda$. If $v$ is also ... $A+B$. eigenvalue of $A^3$ is $\lambda^3$ and the eigenvector is $v^3$ .

Let the $n \times n$ matrix $A$ have an eigenvalue $\lambda$ with corresponding eigenvector $v$.Which of the following statements are true for matrix $A$.$-v$ is an eigen...

GO Classes

154 views

GO Classes asked Apr 3

Linear Algebra
goclasses2025_csda_wq5
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linear-algebra
matrix
eigen-value
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