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Matrices and DeterminantsQuestion and Answers: Page 7

Question Number 82101 Answers: 0 Comments: 2

Make 2 3×3 matrices i and j such that i^2 =j j^2 =i ij=−1

$M a k e 2 3 \times 3 m a t r i c e s i a n d j$ $s u c h t h a t$ $i^{2} = j$ $j^{2} = i$ $i j = - 1$

Question Number 81906 Answers: 0 Comments: 1

Question Number 80830 Answers: 1 Comments: 0

given A a square matrix non singular A≠ I. find A such that A^3 = I

$g i v e n A a s q u a r e m a t r i x n o n$ $s i n g u l a r A \neq I .$ $f i n d A s u c h t h a t A^{3} = I$

Question Number 78670 Answers: 0 Comments: 2

let A= [((a b)),((c d)) ]use the augmented matrix[A I] and elementary row operation to show A^(−1) = (1/(ad bc)) [((a b)),((c d)) ]and show that det(A^(−1) )=(1/(det(A)))

$l e t A = [\begin{matrix} a b \\ c d \end{matrix}] u s e t h e a u g m e n t e d m a t r i x [A I] a n d e l e m e n t a r y r o w o p e r a t i o n t o s h o w A^{- 1} = \frac{1}{a d b c} [\begin{matrix} a b \\ c d \end{matrix}] a n d s h o w t h a t d e t (A^{- 1}) = \frac{1}{d e t (A)}$

Question Number 77565 Answers: 0 Comments: 6

Question Number 76812 Answers: 1 Comments: 0

Given that A and B are 3 × 3 invertible matrices, then (A^(−1) B)^(−1) = A. AB^(−1) B.B^(−1) A C. B^(−1) A^(−1) D. BA^(−1)

$Given that A and B are 3 \times 3 invertible matrices,$ $then {(A^{- 1} B)}^{- 1} =$ $A . {AB}^{- 1}$ $B . B^{- 1} A$ $C . B^{- 1} A^{- 1}$ $D . {BA}^{- 1}$

Question Number 76326 Answers: 2 Comments: 0

Question Number 75814 Answers: 1 Comments: 1

Question Number 75099 Answers: 1 Comments: 4

Given the matrix A = ((1,(−1),1),(0,2,( −1)),(2,3,0) ) and B= ((3,3,(−1)),((−2),(−2),1),((−4),(−5),2) ) find the matrix product AB and BA state the relationship between A and B find also the matrix product BM, where M= ((8),((−7)),(1) ) Hence solve the system of equations: x−y + z = 8, 2y −z =−7, 2x + 3y = 1.

$G i v e n t h e m a t r i x$ $A = (\begin{matrix} 1 & - 1 & 1 \\ 0 & 2 & - 1 \\ 2 & 3 & 0 \end{matrix}) a n d B = (\begin{matrix} 3 & 3 & - 1 \\ - 2 & - 2 & 1 \\ - 4 & - 5 & 2 \end{matrix})$ $f i n d t h e m a t r i x p r o d u c t A B a n d B A$ $s t a t e t h e r e l a t i o n s h i p b e t w e e n A a n d B$ $f i n d a l s o t h e m a t r i x p r o d u c t B M, w h e r e M = (\begin{matrix} 8 \\ - 7 \\ 1 \end{matrix})$ $H e n c e s o l v e t h e s y s t e m o f e q u a t i o n s :$ $x - y + z = 8,$ $2 y - z = - 7,$ $2 x + 3 y = 1 .$

Question Number 74369 Answers: 0 Comments: 0

please state Cramer′s rule

$p l e a s e s t a t e {C r a m e r}^{'} s r u l e$

Question Number 74323 Answers: 0 Comments: 3

Question Number 69954 Answers: 0 Comments: 3

A= (((1 2)),((0 1)) ) find A^n

$A = (\begin{matrix} 1 2 \\ 0 1 \end{matrix}) find A^{n}$

Question Number 68782 Answers: 0 Comments: 0

Let d_n be the determinant of the n×n matrix whose entries, from left to right and then from top to bottom, are cos 1, cos 2, ..., cos n^2 . (For example, d_3 = determinant (((cos 1 cos 2 cos 3)),((cos 4 cos 5 cos 6)),((cos 7 cos 8 cos 9))). The argument of cos is always in radians not degrees.) Evalue lim_(n→∞) d_(n.)

$Let d_{n} be the determinant of the n \times n$ $matrix whose entries, from left to right$ $and then from top to bottom, are$ $c o s 1, c o s 2, . . ., c o s n^{2} . (For example,$ $d_{3} = | \begin{matrix} c o s 1 c o s 2 c o s 3 \\ c o s 4 c o s 5 c o s 6 \\ c o s 7 c o s 8 c o s 9 \end{matrix} | .$ $The argument of c o s is always in radians$ $not degrees .)$ $Evalue \lim_{n \to \infty} d_{n .}$