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+3y=5,2x+6y=8
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.
Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}1&0&0\\0& \cos\alpha& \sin\alpha\\0&\sin\alpha&-\cos\alpha\end{bmatrix}\)
Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}1&-1&2\\0&2&-3\\3&-2&4\end{bmatrix}\)
Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}2&1&3\\4&-1&0\\-7&2&1\end{bmatrix}\)
Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}-1&5\\-3&2\end{bmatrix}\)
Find the inverse of each of the matrices (if it exists). \(\begin{bmatrix}1&0&0\\3&3&0\\5&2&-1\end{bmatrix}\)
Find adjoint of each of the matrices. \(\begin{bmatrix}1&2\\3&4\end{bmatrix}\)
For the matrices A and B, verify that (AB)′=B'A' whereI. A=\(\begin{bmatrix}1\\-4\\3\end{bmatrix}\),B=\(\begin{bmatrix}-1&2&1\end{bmatrix}\)
II. A= \(\begin{bmatrix}0\\1\\2\end{bmatrix}\),B=\(\begin{bmatrix}1&5&7\end{bmatrix}\)
Using Cofactors of elements of second row, evaluate △=\(\begin{vmatrix}5&3&8\\2&0&1\\1&2&3\end{vmatrix}\)
Which of the following is correct?
Choose the correct answer. Let A be a square matrix of order 3×3,then IkAI is equal to
By using properties of determinants, show that: \(\begin{vmatrix}1&x&x^2\\x^2&1&x\\x&x^2&1\end{vmatrix}\)=(1-x3)2
By using properties of determinants, show that: \(\begin{vmatrix}-a^2&ab&ac\\ba&-b^2&bc\\ca&cb&-c^2\end{vmatrix}\)=4a2b2c2
By using properties of determinants ,show that: \(\begin{vmatrix}0&a&-b\\-a&0&-c\\b&c&0\end{vmatrix}\)=0
Using the property of determinants and without expanding, prove that: \(\begin{vmatrix}2&7&65\\3&8&75\\5&9&86\end{vmatrix}\)=0
Using the property of determinants and without expanding, prove that: \(\begin{vmatrix}x&a&x+a\\y&b&y+b\\z&C&z+c\end{vmatrix}=0\)