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
Solve system of linear equations, using matrix method.4x-3y=33x-5y=7
Solve system of linear equations, using matrix method. 2x-y=-2 3x+4y=3
Solve system of linear equations, using matrix method. 5x+2y=4, 7x+3y=5
Examine the consistency of the system of equations. 5x−y+4z=5, 2x+3y+5z=2, 5x−2y+6z=−1
Examine the consistency of the system of equations. 3x-y−2z=2, 2y−z=−1 3x−5y=3
Examine the consistency of the system of equations.x+y+z=12x+3y+2z=2,ax+ay+2az=4
Examine the consistency of the system of equations.x+3y=5,2x+6y=8
If \(A = \begin{bmatrix} \frac{2}{3} & 1 & \frac 53 \\[0.3em] \frac{1}{3} & \frac 23 & \frac{4}{3} \\[0.3em] \frac 73 & 2 & \frac{2}{3} \end{bmatrix}\) and \(B = \begin{bmatrix} \frac{2}{5} & \frac 35 & 1 \\[0.3em] \frac{1}{5} & \frac 25 & \frac{4}{5} \\[0.3em] \frac 75 & \frac 65 & \frac{2}{5} \end{bmatrix}\) then compute 3A-5B.
Examine the consistency of the system of equations.2x-y=5,x+y=4
Examine the consistency of the system of equations. x+2y=2,2x+3y=3
Let A be a nonsingular square matrix of order 3×3.Then IadjAI is equal to
For the matrix A=\(\begin{bmatrix}3&2\\1&1\end{bmatrix}\),find the numbers a and b such that A2+ aA+bI=O.
Let A=\(\begin{bmatrix}3&7\\2&5\end{bmatrix}\)and B=\(\begin{bmatrix}6&8\\7&9\end{bmatrix}\),Verify that (AB)-1=B-1A-1.
Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}1&0&0\\0& \cos\alpha& \sin\alpha\\0&\sin\alpha&-\cos\alpha\end{bmatrix}\)