Write Minors and Cofactors of the elements of following determinants: I. \(\begin{vmatrix}2&-4\\0&3\end{vmatrix}\)
II. \(\begin{vmatrix}a&c\\b&d\end{vmatrix}\)
Find the area of the region bounded by the parabola y=x2 and y=|x|
The area between x=y2 and x=4 is divided into two equal parts by the line x=a, find the value of a.
Find the area of the smaller part of the circle x2+y2=a2 cut off by the line x=a/√2
Find the area of the region in the first quadrant enclosed by x-axis,line x=√3y and the circle x2+y2=4
Verify A(adj A)=(adj A)A=\(\mid A \mid I\).
\(\begin{bmatrix}1&-1&2\\3&0&-2\\1&0&3\end{bmatrix}\)
By using properties of determinants, show that:
\(\begin{vmatrix}a^2+1&ab&ac\\ab&b^2+1&bc\\ca&cb&c^2+1\end{vmatrix}\)=1+a2+b2+c2
Show that points A (a,b+c),B (b,c+a),C (c,a+b) are collinear
Find area of the triangle with vertices at the point given in each of the following:I. (1,0),(6,0),(4,3)II. (2,7),(1,1),(10,8)III. (−2,−3),(3,2),(−1,−8)
If A=\(\begin{bmatrix}3&-2\\4&-2\end{bmatrix}\) and I=\(\begin{bmatrix}1&0\\0&1\end{bmatrix}\),find k so that A2=kA-2I
Show that (i)\(\begin{bmatrix}5&-1\\6&7\end{bmatrix}\)\(\begin{bmatrix}2&1\\3&4\end{bmatrix}\)\(\neq \begin{bmatrix}2&1\\3&4\end{bmatrix}\begin{bmatrix}5&-1\\6&7\end{bmatrix}\)
(ii)\(\begin{bmatrix}1&2&3\\0&1&0\\ 1&1&0\end{bmatrix}\)\(\begin{bmatrix}-1&1&0\\0&-1&1\\ 2&3&4\end{bmatrix}\)\(\neq \) \(\begin{bmatrix}-1&1&0\\0&-1&1\\ 2&3&4\end{bmatrix}\)\(\begin{bmatrix}1&2&3\\0&1&0\\ 1&1&0\end{bmatrix}\)
If F(x)= \(\begin{bmatrix}\cos x&\sin x&0\\\sin x&cos x&0\\0&0&1\end{bmatrix}\)and F(y)=\(\begin{bmatrix}\cos y&-\sin y&0\\\sin y&cos y&0\\0&0&1\end{bmatrix}\),show that F(x)+F(y)=F(x+y)
If x \(\begin{bmatrix}2\\3\end{bmatrix}\)+y \(\begin{bmatrix}-1\\1\end{bmatrix}\)=\(\begin{bmatrix}10\\5\end{bmatrix}\),find values of x and y.
Solve the equation for x,y,z and t if 2\(\begin{bmatrix}x&y\\y&t\end{bmatrix}\)+3\(\begin{bmatrix}1&-1\\0&2\end{bmatrix}\)=3\(\begin{bmatrix}3&5\\4&6\end{bmatrix}\)
Find x and y, if 2\(\begin{bmatrix}1&3\\0&x\end{bmatrix}\)+\(\begin{bmatrix}y&0\\1&2\end{bmatrix}\)=\(\begin{bmatrix}5&6\\1&8\end{bmatrix}\)
Simplify \(\cos\theta\) \(\begin{bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{bmatrix}\)+\(\sin\theta\) \(\begin{bmatrix}\sin\theta&-\cos\theta\\\cos\theta&\sin\theta\end{bmatrix}\)
Verify A(adj A)=(adj A)A=IAII. \(\begin{bmatrix}2&3\\-4&-6\end{bmatrix}\)
Find adjoint of each of the matrices \(\begin{bmatrix}1&-1&2\\2&3&5\\-2&0&1\end{bmatrix}\)
If A=\(\begin{bmatrix}2&3&5\\3&2&-4\\1&1&-2\end{bmatrix}\),find A-1.UsingA-1 solve the system of equations2x-3y+5z=113x+2y-4z=-5x+y-2z=-3
Solve system of linear equations, using matrix method. 2x+3y+3z=5 x-2y+z=-4 3x-y-2z=3