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Recent questions tagged long-answer
Questions
If $ A = \begin{bmatrix} 1 & 2 & -3 \\ 5 & 0 & 2 \\ 1 & -1 & 1 \end{bmatrix} , B = \begin{bmatrix} 3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3 \end{bmatrix} \text{ and } C = \begin{bmatrix} 4 & 1 & 2 \\ 0 & 3 & 2 \\ 1 & -3 & 2 \end{bmatrix} $, then compute $( A + B )$ and $( B - C )$. Also verify that $A + ( B - C ) = ( A + B ) - C. $
cbse
class12
bookproblem
ch3
sec2
q4
p81
easy
long-answer
sec-c
math
asked
Nov 26, 2012
by
pady_1
1
answer
if $ F( x ) = \begin{bmatrix} cos\;x & -sin\;x & 0 \\ sin\;x & cos\;x & 0 \\ 0 & 0 & 1 \end{bmatrix}, $ show that $ F( x )\; F( y ) = F( x + y ). $
cbse
class12
bookproblem
ch3
sec2
q13
p82
easy
long-answer
sec-c
math
asked
Nov 25, 2012
by
pady_1
1
answer
if $ A = \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix} ,$ prove that $ A^3 - 6A^2 + 7A + 2I = 0 $
cbse
class12
bookproblem
ch3
sec2
q16
p82
medium
long-answer
sec-c
math
asked
Nov 25, 2012
by
pady_1
1
answer
A trust fund has Rs 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of: $$ \text{(a) Rs 1800} \qquad \qquad \text{(b) Rs 2000} $$
cbse
class12
bookproblem
ch3
sec2
q19
p82
easy
long-answer
math
sec-b
asked
Nov 25, 2012
by
pady_1
1
answer
The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.
cbse
class12
bookproblem
ch3
sec2
q20
p83
medium
long-answer
sec-b
math
asked
Nov 25, 2012
by
pady_1
1
answer
Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec4
q17
p97
medium
long-answer
sec-c
math
asked
Nov 23, 2012
by
pady_1
1
answer
Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec4
q16
p97
medium
long-answer
sec-c
math
asked
Nov 23, 2012
by
pady_1
1
answer
Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & -3 & 3 \\ 2 & 2 & 3 \\ 3 & -2 & 2 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec4
q15
p97
medium
long-answer
sec-c
math
asked
Nov 23, 2012
by
pady_1
1
answer
if $A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}$ prove that $A^n = \begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \end{bmatrix} , n \in N$.
cbse
class12
bookproblem
ch3
misc
q2
p100
difficult
long-answer
sec-c
math
asked
Nov 23, 2012
by
pady_1
1
answer
If $ A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$ then prove that $ A^n = \begin{bmatrix} 1+2n & -4n \\ n & 1 - 2n \end{bmatrix} $ , where $n$ is any positive integer.
cbse
class12
bookproblem
ch3
misc
q3
p100
medium
long-answer
sec-b
math
asked
Nov 23, 2012
by
pady_1
1
answer
Find the values of $x, y, z $ if the matrix $ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} $ satisfy the equation $A'A = I $
cbse
class12
bookproblem
ch3
misc
q6
p100
medium
long-answer
sec-b
math
asked
Nov 23, 2012
by
pady_1
1
answer
If \(A\) and \(B\) are square matrices of the same order such that \(AB = BA \), then prove by induction that \(AB^n = B^nA \). Further, prove that \( (AB)^n = A^nB^n \: \) for all \( n ∈ N. \)
cbse
class12
bookproblem
ch3
misc
q12
p101
long-answer
difficult
sec-c
math
asked
Nov 22, 2012
by
pady_1
1
answer
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