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Recent questions in Determinants
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CBSE XII
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Math
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Determinants
Evaluate : $\begin{vmatrix} a & b-c & c+b \\ a+c & b & c-a \\ a-b & b+a & c \end{vmatrix} $
cbse
class12
maths
ch4
sec-c
asked
Dec 21, 2016
by
priyanka.c
1
answer
Without expanding show that $\begin{vmatrix} x^2+x & x+1 & x-2 \\ 2x^2 +3x-1 & 3x & 3x-3 \\ x^2+2x+3 & 2x-1 & 2x-1 \end{vmatrix} = xA +B$ Also find A and B.
cbse
class12
maths
ch4
sec-c
asked
Dec 9, 2016
by
priyanka.c
1
answer
Using cofactors of elements of second row, evaluate $\triangle = \begin{vmatrix} 5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3 \end{vmatrix}$
cbse
class12
maths
ch4
sec-e
asked
Dec 5, 2016
by
priyanka.c
1
answer
$ \text{If } \Delta = \begin{vmatrix} a_{11}&a_{12}&a_{13} \\ a_{21}&a_{22}&a_{23} \\ a_{31}&a_{32}&a_{33} \end{vmatrix} \text{ and } A_y \text{ is Cofactor of } a_y \text{, then the value of } a_{11}A_{21}+a_{12}A_{22}+a_{13}A_{23}=? $
cl786
cbse
class12
bookproblem
ch4
sec4
q5
p126
easy
sec-a
math
asked
Feb 11, 2014
by
rvidyagovindarajan_1
1
answer
$ \text{If } \begin{vmatrix} 2 x&5 \\ 8&x \end{vmatrix} = \begin{vmatrix} 4&5 \\ 8&3 \end{vmatrix},then\; x\; is\; equal\; to$
cbse
class12
bookproblem
ch4
sec1
q8
p109
easy
sec-a
math
asked
Jan 31, 2014
by
rvidyagovindarajan_1
1
answer
If $x,y,z$ are all distinct and $\begin{vmatrix}x&x^2&1+x^3\\y&y^2&1+y^3\\z&z^2&1+z^3\end{vmatrix}=0$ then the value of $\;\large\frac{-1}{xyz}$ is
cbse
class12
additionalproblem
ch4
sec-b
medium
math
asked
Jan 30, 2014
by
balaji.thirumalai
1
answer
If $A= \; \begin{bmatrix} 1& 0 &0 \\ 2 & 3 & 4\\ 0&1 & 2 \end{bmatrix}$, then the value of $A.(Adj\:A)$ is?
cbse
class12
ch4
additionalproblem
easy
sec-a
math
asked
Jan 30, 2014
by
rvidyagovindarajan_1
1
answer
Evaluate: $ \begin{vmatrix} (x-2)^2 & (x-1)^2 & x^2 \\ (x-1)^2 & x^2 & (x+1)^2 \\ x^2 & (x+1)^2 & (x+2)^2 \end{vmatrix}$
class12
cbse
easy
additionalproblem
ch4
sec-b
math
asked
Dec 22, 2013
by
balaji.thirumalai
1
answer
If the following matrix is singular, what is the value of $x: \; \begin{bmatrix} -3& -5 &1 \\ 9 & 14 & 1\\ 7+x&29 & -2 \end{bmatrix}$
cbse
class12
ch4
additionalproblem
easy
sec-a
math
asked
Dec 22, 2013
by
balaji.thirumalai
1
answer
determinants
asked
Oct 25, 2013
by
sharon.r.varghese_1
0
answers
Using matrices, solve the following system of equations:$x+\frac{2}{y}+3xz=-1,2x-\frac{4}{y}-3xz=3,3x+\frac{6}{y}-2xz=4$
cbse
class12
additionalproblem
ch4
sec-c
math
asked
Apr 8, 2013
by
meena.p
1
answer
Find the area of the triangle where vertices are $A(11,7),B(5,5)\; and\; C(-1,3)$
cbse
class12
additionalproblem
ch4
sec-b
math
asked
Apr 8, 2013
by
meena.p
1
answer
Solve for $x$ if $\begin{vmatrix} 1 & 4 & 4 \\ 1 & -2 & 1 \\ 1 & 2x & x^2 \end{vmatrix} =0 $
cbse
class12
additionalproblem
ch4
sec-a
math
asked
Apr 8, 2013
by
meena.p
1
answer
Show that $A=\begin{bmatrix} 1 & log_x\;y & log_x\;z \\ log_y\;x & 1 & log_y\;z \\ log_z\;x & log_z\;y & 1 \end{bmatrix}=0$
cbse
class12
additionalproblem
ch4
sec-b
math
asked
Apr 6, 2013
by
meena.p
1
answer
Show that $A=\begin{bmatrix} xc_{r} & xc_{r+1} & xc_{r+2} \\ yc_r & yc_{r+1} & yc_{r+2} \\ zc_r & zc_{r+1} & zc_{r+2} \end{bmatrix}=\begin{bmatrix} xc_{r} & x+1c_{r+1} & x+2c_{r+2} \\ yc_r & y+1c_{r+1} & y+2c_{r+2} \\ zc_r & z+1c_{r+1} & z+2c_{r+2} \end{bmatrix}$
cbse
class12
additionalproblem
ch4
sec-b
math
asked
Apr 5, 2013
by
meena.p
1
answer
Solve the following system of equations by matrix method:x+2y+z=7,x+3z=11,2x-3y=1.
cbse
class12
additionalproblem
ch4
sec-c
math
asked
Apr 5, 2013
by
sreemathi.v
1
answer
Using properties of determinants, evaluate $A=\begin{vmatrix}43 & 1 & 6\\35 & 7 & 4\\17 & 3 &2\end{vmatrix}$
cbse
class12
additionalproblem
ch4
sec-a
math
asked
Apr 5, 2013
by
sreemathi.v
1
answer
If a,b,c are positive and unequal,show that the value of the determinant $\Delta=\begin{vmatrix}a & b & c\\b & c & a\\c & a & b\end{vmatrix}$ is negative.
cbse
class12
additionalproblem
ch4
sec-c
difficult
math
asked
Apr 5, 2013
by
sreemathi.v
1
answer
The sum of three numbers is 6.If we multiply the third number by 2 and add the first number to the result,we get 7.By adding second and third numbers to three times the first number we get 12.Use determinants to find the numbers.
cbse
class12
additionalproblem
ch4
sec-c
difficult
math
asked
Apr 5, 2013
by
sreemathi.v
1
answer
Evaluate : $ \begin{vmatrix} 1 & log_ba \\ log_ab & 1 \end{vmatrix}$
cbse
class12
ch4
q4
sec-a
additionalproblem
medium
math
asked
Apr 3, 2013
by
meena.p
1
answer
If $\begin{vmatrix}4+x& 4-x & 4-x\\4-x & 4+x & 4-x\\4-x & 4-x & 4+x\end{vmatrix}$,then find the values of x.
cbse
class12
ch4
sec-b
q13
p78
shortanswer
exemplar
medium
math
asked
Mar 18, 2013
by
sreemathi.v
1
answer
If the coordinates of the vertices of an equilateral triangle with sides of length 'a' are $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ then \[{\begin{vmatrix}x_1 & y_1 &1\\x_2 & y_2 &1\\x_3 & y_3 & 1\end{vmatrix}}^2=\frac{3a^4}{4}.\]
cbse
class12
ch4
sec-b
q11
p78
short-answer
exemplar
difficult
math
asked
Mar 15, 2013
by
sreemathi.v
1
answer
If A+B+C=0,then prove that $\begin{vmatrix}1& cosC &cos B\\cos C& 1 &cos A\\cos B & cos A &1\end{vmatrix}=0.$
cbse
class12
ch4
sec-b
q10
p78
short-answer
exemplar
medium
math
asked
Mar 15, 2013
by
sreemathi.v
1
answer
Using the properties of determinants,\[\begin{vmatrix}a^2+2a &2a+1 & 1\\2a+1 & a+2 & 1\\3 & 3 & 1\end{vmatrix}=(a-1)^3\]
cbse
class12
ch4
sec-b
q9
p78
short-answer
exemplar
easy
math
asked
Mar 15, 2013
by
sreemathi.v
1
answer
Using matrices,solve the system of linear equations,\[2x-y+z=3\]\[-x+2y-z=-4\]\[x-y+2z=1\]
cbse
class12
additionalproblem
ch4
sec-c
math
asked
Mar 14, 2013
by
sreemathi.v
1
answer
Using properties of determinants,solve for x,\[\begin{vmatrix}a+x & a-x& a-x\\a-x & a+x & a-x\\a-x & a-x & a+x\end{vmatrix}=0\]
cbse
class12
additionalproblem
ch4
sec-b
math
asked
Mar 13, 2013
by
sreemathi.v
1
answer
Given a square matrix $A$, let $adj (A)$ be the adjoint, and $C$ be the cofactor matrix of $A$. Which of the following is a representation of the adjoint of A, i.e, $adj (A) = ?$
cbse
class12
ch4
concepts
toolbox
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
If the Minor of an element $a_{ij}$ is denoted by $M_{ij}$ and the cofactor of an element $a_{ij}$ is denoted by $A_{ij}$ then, which of the following is true?
cbse
toolbox
concepts
ch4
class12
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
If the Minor of an element $a_{ij}$ is denoted by $M_{ij}$ and the cofactor of an element $a_{ij}$ is denoted by $A_{ij}$ then, which of the following is true?
cbse
class12
ch4
concepts
toolbox
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
What is the area of a triangle with vertices (x1, y1), (x2, y2) and (x3, y3)?
cbse
class12
concepts
toolbox
ch4
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
True or False: If to each element of a row (or a column) of a determinant the equimultiples of corresponding elements of other rows (columns) are added, then value of determinant remains same.
cbse
class12
concepts
toolbox
ch4
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
True or False: The determinant of the product of matrices is equal to product of the individual determinants, $det(AB) = det(A).det(B)$
cbse
class12
concepts
toolbox
ch4
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
If we multiply one row a matrix by k, i.e, $\begin{vmatrix} ka& kb\\ c& d\end{vmatrix}$, then which of the following is also the value of the determinant?
class12
cbse
toolbox
concepts
ch4
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
If any two rows or any two columns in a determinant are identical (or proportional), then which of the following is true?
toolbox
concepts
class12
cbse
ch4
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
In a square matrix, If we interchange any two rows (or columns),which of the following is true?
cbse
class12
concepts
toolbox
ch4
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
True or False: Any square matrix A and its transpose have the same determinant.
cbse
class12
concepts
toolbox
ch4
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
What is the value of the determinant of the following 3x3 matrix: $\begin{vmatrix} a&b&c \\ d&e&f \\ g&h&i \end{vmatrix}?$
cbse
class12
concepts
toolbox
ch4
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
What is the determinant of 2x2 matrix $\begin{vmatrix} a & b\\c & d\end{vmatrix}?$
cbse
class12
ch4
concepts
toolbox
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
Fill in the blank: For every ______ matrix A of order n, we can associate a number called determinant of the matrix A, written as det A, where aij is the (i, j)th element of A.
cbse
toolbox
class12
concepts
ch4
math
asked
Mar 12, 2013
by
balaji.thirumalai
1
answer
By using the properties of determinants show that $ (ii) \begin{vmatrix} x+y+2z&x&y \\ z&y+z+2x&y \\ z&x&z+x+2y \end{vmatrix} = 2(x+y+z)^3 $
cbse
class12
bookproblem
ch4
sec2
q11
q11-2
p120
medium
sec-b
math
asked
Mar 11, 2013
by
sreemathi.v
1
answer
By using the properties of determinants show that $ (ii) \begin{vmatrix} y+k&y&y \\ y&y+k&y \\ y&y&y+k \end{vmatrix} = k^2 (3y+k)$
cbse
class12
bookproblem
ch4
sec2
q10
q10-2
p120
medium
sec-b
math
asked
Mar 11, 2013
by
sreemathi.v
1
answer
Write Minors and Cofactors of the elements of following determinants: $ (ii) \quad \begin{vmatrix} 1&0&4 \\ 3&5&-1 \\ 0&1&2 \end{vmatrix} $
cbse
class12
bookproblem
ch4
sec4
q2
q2-2
p126
easy
sec-a
math
asked
Mar 6, 2013
by
sreemathi.v
1
answer
Write Minors and Cofactors of the elements of following determinants: $ \quad \begin{vmatrix} a&c \\ b&d \end{vmatrix}$
cbse
class12
bookproblem
ch4
sec4
q1
q1-2
p126
easy
sec-a
math
asked
Mar 6, 2013
by
sreemathi.v
1
answer
By using the properties of determinants show that $ (ii) \quad \begin{vmatrix} 1&1&1 \\ a&b&c \\ a^3&b^3&c^3 \end{vmatrix} = (a-b)(b-c)(c-a)(a+b+c) $
cbse
class12
bookproblem
ch4
sec2
q8
q8-2
p120
easy
sec-b
math
asked
Mar 6, 2013
by
sreemathi.v
1
answer
Find the values of $x$, if $ \text{: } \begin{vmatrix} 2&3 \\ 4&5 \end{vmatrix} = \begin{vmatrix} x&3 \\ 2x&5 \end{vmatrix}$
cbse
class12
bookproblem
ch4
sec1
q7
q7-2
p106
easy
sec-a
math
asked
Mar 6, 2013
by
sreemathi.v
1
answer
Evaluate the determinants: $ \begin{vmatrix} 2&-1&2 \\ 0&2&-1 \\3&-5&0 \end{vmatrix}$
cbse
class12
bookproblem
ch4
sec1
q5
q5-4
p108
easy
sec-a
math
asked
Mar 6, 2013
by
sreemathi.v
1
answer
Evaluate the determinants: $ \begin{vmatrix} 0&1&2 \\ -1&0&3 \\-2&3&0 \end{vmatrix}$
cbse
class12
bookproblem
ch4
sec1
q5
q5-3
p108
easy
sec-a
math
asked
Mar 6, 2013
by
sreemathi.v
1
answer
Evaluate the determinants: $ \begin{vmatrix} 3&-4&5 \\ 1&1&-2 \\2&3&1 \end{vmatrix}$
cbse
class12
bookproblem
ch4
sec1
q5
q5-2
p108
easy
sec-a
math
asked
Mar 6, 2013
by
sreemathi.v
1
answer
$ \text{Evaluate the determinants: } \text{(ii): } \begin{vmatrix} x^2-x+1&x-1\\x+1&x+1 \end{vmatrix}$
cbse
class12
bookproblem
ch4
sec1
q2
q2-2
p108
easy
sec-a
math
asked
Mar 6, 2013
by
sreemathi.v
1
answer
Let A = $\begin{bmatrix} 1 & -2 & 1\\ -2 & 3 & 1\\ 1 & 1 & 5 \end{bmatrix}$. Verify that \[\] $(ii)\big(A^{-1}\big)^{-1}$
cbse
class12
bookproblem
ch4
misc
q8
q8-2
p142
easy
sec-b
math
asked
Mar 1, 2013
by
sreemathi.v
1
answer
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