# Recent questions tagged rank

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Let $A$ and $B$ be $n \times n$ matrices.
Let $A$ and $B$ be $n \times n$ matrices.Let $A$ and $B$ be $n \times n$ matrices. a) Show that the $\operatorname{rank}(A B) \leq \operatorname{rank}(A)$. Give an example where stric ...
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Let $A, B$, and $C$ be $n \times n$ matrices.
Let $A, B$, and $C$ be $n \times n$ matrices.Let $A, B$, and $C$ be $n \times n$ matrices. a) If $A^{2}$ is invertible, show that $A$ is invertible. NOTE: You cannot naively use the f ...
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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"?
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"?Let $A$ be an $n \times n$ matrix of real or complex numbers. Which of the following statements are equivalent to: &quot;the matrix $A$ is inver ...
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If $A$ is a $5 \times 5$ matrix with $\operatorname{det} A=-1$, compute $\operatorname{det}(-2 A)$.
If $A$ is a $5 \times 5$ matrix with $\operatorname{det} A=-1$, compute $\operatorname{det}(-2 A)$.If $A$ is a $5 \times 5$ matrix with $\operatorname{det} A=-1$, compute $\operatorname{det}(-2 A)$. ...
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$$\text { The rank of the coefficient matrix } A=\left[\begin{array}{ccc} 1 & 2 & -3 \\ 3 & -1 & 5 \\ 4 & 1 & 2 \end{array}\right] \text { equals: }$$ \text { The rank of the coefficient matrix } A=\left\begin{array}{ccc} 1 &amp; 2 &amp; -3 \\ 3 &amp; -1 &amp; 5 \\ 4 &amp; 1 &amp; 2 ...
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The augmented matrix of a system $A X=B$ has been transformed using elementary row operations to ...
The augmented matrix of a system $A X=B$ has been transformed using elementary row operations to ... \begin{aligned} &amp;\text { The augmented matrix of a system } A X=B \text { has been transformed using elementary row }\\ &amp ...
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$$\text { Let matrices } A \text { and } B \text { be given by } A=\left[\begin{array}{lll} a & b & c \\ d & e & f \\ g & h & i \end{array}\right]$$ \begin{aligned} &amp;\text { Let matrices } A \text { and } B \text { be given by } A=\left\begin{array}{lll} a &amp; b &amp; c \\ d ...
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How do I calculate percentile rank?
How do I calculate percentile rank?How do I calculate percentile rank? ...
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Do scholars rank Abraham Lincoln among the top three presidents?