Choose the correct answer.Let A=\(\begin{bmatrix}1&sin\theta&1\\-sin\theta&1&sin\theta\\-1&-sin\theta&1\end{bmatrix}\),\(where 0≤\theta≤2\pi,then\)
Prove that\(\begin{vmatrix} a^2&bc &ac+c^2 \\ a^2+ab&b^2 &ac\\ ab&b^2+bc &c^2 \end{vmatrix}=4a^2b^2c^2\)
Solve the equation \(\begin{vmatrix} x+a &x &x \\ x &x+a &x \\ x&x &x+a \end{vmatrix}=0\) , a≠0
If a,b, and c are real numbers and determinant \(\Delta = \begin{vmatrix} b+c &c+a &a+b \\ c+a&a+b &b+c \\ a+b&b+c &c+a \end{vmatrix}\)Show that either a+b+c=0 or a=b=c.
Prove that the determinant \(\begin{vmatrix} x &sin\theta &cos\theta \\ -sin\theta&-x &1 \\ cos\theta&1 &x \end{vmatrix}\) is independent of θ.
If A is an invertible matrix of order 2,then det(A-1) is equal to
Write Minors and Cofactors of the elements of following determinants: I. \(\begin{vmatrix}2&-4\\0&3\end{vmatrix}\)
II. \(\begin{vmatrix}a&c\\b&d\end{vmatrix}\)
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)
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
Solve system of linear equations, using matrix method.x-y+z=42x+y-3z=0 x+y+z=2
Solve system of linear equations, using matrix method.2x+y+z=1x-2y-z=\(\frac{3}{2}\)3y-5z=9