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For non-zero real numbers one uses \(\frac{1}{a}-\frac{1}{b}=\frac{b-a}{a b}\). Verify the following analog for invertible matrices \(A, B\) :
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Show that \(\operatorname{trace}(A B C)=\operatorname{trace}(C A B)=\operatorname{trace}(B C A)\).
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Show that \(\operatorname{trace}(A B C)=\operatorname{trace}(C A B)=\operatorname{trace}(B C A)\).Let \(A, B\), and \(C\) be any \(n \times n\) matrices. a) Show that \(\operatorname{trace}(A B)=\operatorname{trace}(B A)\). b) Show that \(\operator ...
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asked in Mathematics 14 minutes ago
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Find a real \(2 \times 2\) matrix \(A\) (other than \(A=I\) ) such that \(A^{5}=I\).
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For which real numbers \(x\) do the vectors: \((x, 1,1,1),(1, x, 1,1),(1,1, x, 1),(1,1,1, x)\) not form a basis of \(\mathbb{R}^{4}\) ?
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How do I convert decimal numbers to binary numbers?
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How do I convert decimal numbers to binary numbers?How do I convert decimal numbers to binary numbers? ...
by Pieter SIlver Status
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asked in Mathematics 1 day ago
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Find the sum of the multiples of 3 between 28 and \(112 .\)
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Find the sum of the multiples of 3 between 28 and \(112 .\)Find the sum of the multiples of 3 between 28 and \(112 .\) ...
by Pieter SIlver Status
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asked in Mathematics Jan 17
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Find the constant second difference for the following sequence: \[ 7 ; 4 ;-3 ;-14 ; \ldots \]
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Find the common second difference for the following sequence: \[ -13 ;-25 ;-43 ;-67 ; \ldots \]
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Find the common second difference for the following sequence: \[ -7 ;-15 ;-25 ;-37 ; \ldots \]
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What is aleph?
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What is aleph?What is aleph? ...
by Pieter SIlver Status
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asked in Mathematics Jan 15
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Evaluate \(1,6 \times 10^{-19} \times 3,2 \times 10^{-19} \div 5 \times 10^{-21}\)
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Evaluate \(1,99 \times 10^{-26}+1,67 \times 10^{-27}-2,79 \times 10^{-25}\)
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How do ISBN numbers apply dot products?
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How do ISBN numbers apply dot products? How do ISBN numbers apply dot products?   ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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The expression $(1+\sqrt{3} i)^{-4}$ in standard form is given by:
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The expression $(1+\sqrt{3} i)^{-4}$ in standard form is given by:The expression $(1+\sqrt{3} i)^{-4}$ in standard form is given by:   A. $-64$ B. $-2^{5} i$ C. 16 D. $-2-2 \sqrt{3} i$ E. $-\dfrac{1}{32}+\ ...
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asked in Mathematics Jan 13
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De Moivre's Theorem gives $\cos 3 \theta$ as:
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De Moivre's Theorem gives $\cos 3 \theta$ as:De Moivre's Theorem gives $\cos 3 \theta$ as: ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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The complex number $i^{19}$ is equal to
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The complex number $i^{19}$ is equal toThe complex number $i^{19}$ is equal to   A) 1 B) $-1$ C) i D) $-i$ E) none of the above ...
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asked in Mathematics Jan 13
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The complex number $\frac{1-2 i}{1+2 i}$ is equal to
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The complex number $\frac{1-2 i}{1+2 i}$ is equal toThe complex number $\dfrac{1-2 i}{1+2 i}$ is equal to   A) $\dfrac{3}{5}+\dfrac{4}{5} i$ B) $-\dfrac{3}{5}+\dfrac{4}{5} i$ C) $\dfrac{3}{5}-\ ...
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asked in Mathematics Jan 13
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Solve the equation $$ z^{3}+8 i=0 $$
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Solve the equation $$ z^{3}+8 i=0 $$Solve the equation $$ z^{3}+8 i=0 $$ ...
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asked in Mathematics Jan 13
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Interactive Quiz - Rounding Off Numbers Quiz
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Interactive Quiz - Rounding Off Numbers Quiz Interactive Quiz - Rounding Off Numbers Quiz   ...
by MathsGee Platinum
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asked in Mathematics Jan 11
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Speak the answer. What is 2 + 2 ?
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Speak the answer. What is 2 + 2 ? Speak the answer. What is 2 + 2 ?     ...
by MathsGee Platinum
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asked in Mathematics Jan 11
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Consider the sequence: \[ \frac{1}{2} ; 4 ; \frac{1}{4} ; 7 ; \frac{1}{8} ; 10 ; \ldots \ldots \]
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Consider the sequence: \[ \frac{1}{2} ; 4 ; \frac{1}{4} ; 7 ; \frac{1}{8} ; 10 ; \ldots \ldots \]Consider the sequence: \ \frac{1}{2} ; 4 ; \frac{1}{4} ; 7 ; \frac{1}{8} ; 10 ; \ldots \ldots \ a) If the pattern continues in the same way, write ...
by Pieter SIlver Status
(18,309 points)
asked in Mathematics Jan 11
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