# Recent questions tagged algebra

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Let $A(t)$ be a family of invertible real matrices depending on the real parameter $t$ and assume they are invertible.
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Let $A(t)$ be a family of invertible real matrices depending on the real parameter $t$ and assume they are invertible.Let $A(t)$ be a family of invertible real matrices depending on the real parameter $t$ and assume they are invertible. Show that the inverse matri ...
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Let $A$ and $B$ be $n \times n$ matrices. If $A+B$ is invertible, show that $A(A+B)^{-1} B=$ $B(A+B)^{-1} A$. [Don't assume that $A B=B A$ ].
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Let $A$ and $B$ be $n \times n$ matrices. If $A+B$ is invertible, show that $A(A+B)^{-1} B=$ $B(A+B)^{-1} A$. [Don't assume that $A B=B A$ ].Let $A$ and $B$ be $n \times n$ matrices. If $A+B$ is invertible, show that $A(A+B)^{-1} B=$ $B(A+B)^{-1} A$. Don't assume that $A B=B A ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove that \(A$ is invertible and $B A=I$ as well.
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Prove that $A$ is invertible and $B A=I$ as well.Suppose that $A$ is an $n \times n$ matrix and there exists a matrix $B$ so that \ A B=I \text {. } \ Prove that $A$ is invertible and $B A ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 For each of the following, answer TRUE or FALSE. If the statement is false in even a single instance, then the answer is FALSE. 0 answers 3 views For each of the following, answer TRUE or FALSE. If the statement is false in even a single instance, then the answer is FALSE.For each of the following, answer TRUE or FALSE. If the statement is false in even a single instance, then the answer is FALSE. There is no need to ju ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 At noon the minute and hour hands of a clock coincide. 0 answers 5 views At noon the minute and hour hands of a clock coincide.At noon the minute and hour hands of a clock coincide. a) What in the first time, \(T_{1}$, when they are perpendicular? b) What is the next time, \ ...
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Do I need to know linear algebra for data science?
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Do I need to know linear algebra for data science?Do I need to know linear algebra for data science? ...
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In mathematics/algebra, what is the difference between $|x|$ and $||x||$?
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In mathematics/algebra, what is the difference between $|x|$ and $||x||$?In mathematics/algebra, what is the difference between $|x|$ and $||x||$? ...
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If A is an $n\times n$ matrix and u and v are $n\times 1$ matrices, then prove that $\boldsymbol{A u} \cdot \mathbf{v}=\mathbf{u} \cdot \boldsymbol{A}^{T} \mathbf{v}$
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If A is an $n\times n$ matrix and u and v are $n\times 1$ matrices, then prove that $\boldsymbol{A u} \cdot \mathbf{v}=\mathbf{u} \cdot \boldsymbol{A}^{T} \mathbf{v}$If A is an $n\times n$ matrix and u and v are $n\times 1$ matrices, then prove that $\boldsymbol{A u} \cdot \mathbf{v}=\mathbf{u} \cdot \boldsymbol{A} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The system of linear equations has $$\left\{\begin{array}{l} x-2 y+z=1 \\ -2 x+4 y-2 z=-3 \\ -x+2 y-z=-2 \end{array}\right.$$ 0 answers 6 views The system of linear equations has $$\left\{\begin{array}{l} x-2 y+z=1 \\ -2 x+4 y-2 z=-3 \\ -x+2 y-z=-2 \end{array}\right.$$The system of linear equations has $$\left\{\begin{array}{l} x-2 y+z=1 \\ -2 x+4 y-2 z=-3 \\ -x+2 y-z=-2 \end{array}\right.$$ &nbsp; A) infinitely ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let$A$and$B$be$n \times n$matrices. Which of the following is true? 0 answers 4 views Let$A$and$B$be$n \times n$matrices. Which of the following is true?Let$A$and$B$be$n \times n$matrices. Which of the following is true? &nbsp; A)$\operatorname{det}(A)=\operatorname{det}(-A)$B)$\operatornam ...
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$$\text { Write the system }\left\{\begin{array}{l} z=x+y \\ x-y=3 \text { in the form } A X=B \text {. Then } \\ x=-y \end{array}\right.$$
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$$\text { Write the system }\left\{\begin{array}{l} z=x+y \\ x-y=3 \text { in the form } A X=B \text {. Then } \\ x=-y \end{array}\right.$$ \text { Write the system }\left\{\begin{array}{l} z=x+y \\ x-y=3 \text { in the form } A X=B \text {. Then } \\ x=-y \end{array}\righ ...
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Let $A$ be an $n \times n$ matrix with $I_{n}$ the identity matrix. The statement det $A \neq 0$ is equivalent to:
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Let $A$ be an $n \times n$ matrix with $I_{n}$ the identity matrix. The statement det $A \neq 0$ is equivalent to:Let $A$ be an $n \times n$ matrix with $I_{n}$ the identity matrix. The statement det $A \neq 0$ is equivalent to: &nbsp; A. All the given options a ...
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The system of linear equations $$\begin{gathered} x-2 y+z=1 \\ -2 x+4 y-2 z=-3 \\ -x+2 y-z=-2 \end{gathered}$$
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The system of linear equations $$\begin{gathered} x-2 y+z=1 \\ -2 x+4 y-2 z=-3 \\ -x+2 y-z=-2 \end{gathered}$$The system of linear equations $$\begin{gathered} x-2 y+z=1 \\ -2 x+4 y-2 z=-3 \\ -x+2 y-z=-2 \end{gathered}$$ has &nbsp; A) infinitely many solut ...
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Let $A$ and $B$ be two square invertible matrices of the same order. Then $\left((A B)^{T}\right)^{-1}$ is equal to
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Let $A$ and $B$ be two square invertible matrices of the same order. Then $\left((A B)^{T}\right)^{-1}$ is equal toLet $A$ and $B$ be two square invertible matrices of the same order. Then $\left((A B)^{T}\right)^{-1}$ is equal to &nbsp; A) \$\left(B^{T}\right)^{- ...
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What is the fundamental theorem of algebra?
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What is the fundamental theorem of algebra?What is the fundamental theorem of algebra? ...
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Is algebra easier than calculus?
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Is algebra easier than calculus?Is algebra easier than calculus? ...
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Prove that $x^2+2xy+y^2$ cannot be negative
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Prove that $x^2+2xy+y^2$ cannot be negativeProve that &nbsp;$x^2+2xy+y^2$ cannot be negative ...
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Without using a calculator, determine the value of: $\sum_{y=3}^{10} \frac{1}{y-2}-\sum_{y=3}^{10} \frac{1}{y-1}$
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Without using a calculator, determine the value of: $\sum_{y=3}^{10} \frac{1}{y-2}-\sum_{y=3}^{10} \frac{1}{y-1}$Without using a calculator, determine the value of: \\sum_{y=3}^{10} \frac{1}{y-2}-\sum_{y=3}^{10} \frac{1}{y-1}\ ...
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Find the value of $m$ if: $\sum_{k=1}^{m} 3(2)^{k-1}=93$
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Find the value of $m$ if: $\sum_{k=1}^{m} 3(2)^{k-1}=93$Find the value of $m$ if: \ \sum_{k=1}^{m} 3(2)^{k-1}=93 \ ...
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What is the value of $m$ for which: $\sum_{k=1}^{m} 5(3)^{k-1}=65$
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What is the value of $m$ for which: $\sum_{k=1}^{m} 5(3)^{k-1}=65$What is the value of $m$ for which: \ \sum_{k=1}^{m} 5(3)^{k-1}=65 \ ...
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Evaluate: $\sum_{n=4}^{70}(2 n-4)$
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Evaluate: $\sum_{n=4}^{70}(2 n-4)$Evaluate: \ \sum_{n=4}^{70}(2 n-4) \ ...
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compare a and b
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compare a and b compare a and b ordre sur les reels puisances please&nbsp; help ...
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Find the values of $p$ and $q$
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Find the values of $p$ and $q$\ \mathrm{f}(x)=x^{3}+6 x^{2}+p x+q \ Given that $\mathrm{f}(4)=0$ and $\mathrm{f}(-5)=36$ (a) Find the values of $p$ and $q$ (b) Factoris ...
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Expand and Simplify: $(3 x-2)(x-5)^{2}$
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Expand and Simplify: $(3 x-2)(x-5)^{2}$Expand and Simplify: $(3 x-2)(x-5)^{2}$ ...
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Expand and Simplify: $(2 x-1)(x+2)(x-3)$
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Expand and Simplify: $(2 x-1)(x+2)(x-3)$Expand and Simplify: $(2 x-1)(x+2)(x-3)$ ...
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