Matrices and Determinants – Page 25

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Tinku Tara June 3, 2023 Matrices and Determinants

Question Number 11 by user1 last updated on 25/Jan/15 $Evaluate :$ $| \begin{matrix} x^{2} - x + 1 & x - 1 \\ x + 1 & x + 1 \end{matrix} |$ Answered by user1 last updated on 30/Oct/14 $$=\left[\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)\left({x}+\mathrm{1}\right)−\left({x}+\mathrm{1}\right)\left({x}−\mathrm{1}\right)\right] \…

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Tinku Tara June 3, 2023 Matrices and Determinants

Question Number 13 by user1 last updated on 25/Jan/15 $Expand the determnent$ $△ = | \begin{matrix} a & h & g \\ h & b & f \\ g & f & c \end{matrix} |$ Answered by user1 last updated on 30/Oct/14 $Expanding by 1^{st} row, we have :$ $$\bigtriangleup={a}\centerdot $| \begin{matrix} b & f \\ f & c \end{matrix} |$ −{h}\centerdot $| \begin{matrix} h & f \\ g & c \end{matrix} |$ +{g}\centerdot $| \begin{matrix} h & b \\ g & f \end{matrix} |$ …

If-A-2-1-3-4-1-0-and-B-1-1-0-2-5-0-verify-that-AB-B-A-

Tinku Tara June 3, 2023 Matrices and Determinants

Question Number 7 by user1 last updated on 25/Jan/15 $If A = [\begin{matrix} 2 & 1 & 3 \\ 4 & 1 & 0 \end{matrix}] a n d B = [\begin{matrix} 1 & - 1 \\ 0 & 2 \\ 5 & 0 \end{matrix}],$ $verify that {(A B)}^{'} = B^{'} A^{'}$ Answered by user1 last updated on 30/Oct/14 $We have$ $${AB}= $[\begin{matrix} 2 & 1 & 3 \\ 4 & 1 & 0 \end{matrix}]$ \centerdot $[\begin{matrix} 1 & - 1 \\ 0 & 2 \\ 5 & 0 \end{matrix}]$ \…

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Tinku Tara June 3, 2023 Matrices and Determinants

Question Number 9 by user1 last updated on 25/Jan/15 $Let A = [\begin{matrix} 0 & - \tan \frac{x}{2} \\ \tan \frac{x}{2} & 0 \end{matrix}] and I is the$ $identity matrix of order 2 . Show that$ $(I + A) = (I - A) \cdot [\begin{matrix} \cos x & - \sin x \\ \sin x & \cos x \end{matrix}] .$ Answered by user1 last updated on 30/Oct/14 $$\mathrm{Let}\:\:\:\:\mathrm{tan}\:\frac{{x}}{\mathrm{2}}={t} \…

Question-143270

Tinku Tara June 3, 2023 Matrices and Determinants 0 Comments

Question Number 143270 by SLVR last updated on 12/Jun/21 Answered by Olaf_Thorendsen last updated on 12/Jun/21 $B (i, j) ⩾ 1$ $$\mathrm{Let}\:{c}_{{ij}} \:=\:\mathrm{B}^{\mathrm{2}} \left({i},{j}\right)\:=\:\underset{{p}=\mathrm{1}} {\overset{\lambda} {\sum}}\underset{{q}=\mathrm{1}} {\overset{\lambda} {\sum}}{b}_{{ip}}…

Question-143200

Tinku Tara June 3, 2023 Matrices and Determinants 0 Comments

Question Number 143200 by Guddone last updated on 11/Jun/21 Answered by Dwaipayan Shikari last updated on 11/Jun/21 $2 x + 3 y = [\begin{matrix} 2 3 \\ 4 0 \end{matrix}] \Rightarrow 6 x + 9 y = [\begin{matrix} 6 9 \\ 12 0 \end{matrix}] \to (a)$ $3 x + 2 y = [\begin{matrix} 2 - 2 \\ - 1 5 \end{matrix}] \Rightarrow 6 x + 4 y = [\begin{matrix} 4 - 4 \\ - 2 10 \end{matrix}] \to (b)$ $a - b \Rightarrow 5 y = [\begin{matrix} 2 13 \\ 14 - 10 \end{matrix}] \Rightarrow y = [\begin{matrix} \frac{2}{5} \frac{13}{5} \\ \frac{14}{5} - 2 \end{matrix}]$ $${x}=\frac{\mathrm{1}}{\mathrm{2}}\left( $[\begin{matrix} 2 3 \\ 4 0 \end{matrix}]$ − $[\begin{matrix} \frac{6}{5} \frac{39}{5} \\ \frac{42}{5} - 6 \end{matrix}]$ \right)=\frac{\mathrm{1}}{\mathrm{2}}\left( $[\begin{matrix} \frac{4}{5} \frac{- 24}{5} \\ \frac{- 22}{5} 6 \end{matrix}]$ \right)= $[\begin{matrix} \frac{2}{5} - \frac{12}{5} \\ - \frac{11}{5} 3 \end{matrix}]$ \…

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Tinku Tara June 3, 2023 Matrices and Determinants 0 Comments

Question Number 12046 by 7991 last updated on 10/Apr/17 $h o w m u c h m a t r i c e s o f i n t e g e r s n u m b e r$ $A = [\begin{matrix} a & b \\ c & d \end{matrix}] i f A^{2} + A = 2 I, c = 0, d e t (A) = 4$ Answered by sma3l2996 last updated on 10/Apr/17 $${A}^{\mathrm{2}} = $[\begin{matrix} a & b \\ 0 & d \end{matrix}]$ $[\begin{matrix} a & b \\ 0 & d \end{matrix}]$ =\begin{bmatrix}{{a}^{\mathrm{2}} }&{{ab}+{db}}\{\mathrm{0}}&{{d}^{\mathrm{2}}…

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Tinku Tara June 3, 2023 Matrices and Determinants 0 Comments

Question Number 12044 by 7991 last updated on 10/Apr/17 $A \in M_{n \times n}$ $A^{2} = A$ ${(I + A)}^{- 1} = \dots . ? ? ?$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 10/Apr/17…

Question-77565

Tinku Tara June 3, 2023 Matrices and Determinants 0 Comments

Question Number 77565 by TawaTawa last updated on 07/Jan/20 Commented by MJS last updated on 07/Jan/20 $I {don}^{'} t think that A^{B} for matrices A, B is$ $defined . I only know A^{n} with n \in N; A^{- n} is$ $$\mathrm{only}\:\mathrm{possible}\:\mathrm{if}\:\mathrm{the}\:\mathrm{inverse}\:\mathrm{matrix}\:{A}^{−\mathrm{1}} \:\mathrm{exists}…

A-M-2016-2016-with-the-entries-a-ij-0-if-i-j-2016-1-if-i-j-2016-find-the-determinant-

Tinku Tara June 3, 2023 Matrices and Determinants 0 Comments

Question Number 11958 by 7991 last updated on 07/Apr/17 $A \in M_{2016 \times 2016}$ $w i t h t h e e n t r i e s a_{i j} {_{0, i f i + j \neq 2016}^{1, i f i + j = 2016}$ $f i n d t h e d e t e r m i n a n t ? ?$ Commented by prakash jain last…

Category: Matrices and Determinants