Search & Filtering
Use Cramer’s rule to solve for y without solving for x, z and w in the system
2w + x + y + z = 3
−8w − 7x − 3y + 5z = −3
w + 4x + y + z = 6
w + 3x + 7y − z = 1
Give an example of 2 × 2 matrix with non-zero entries that has no inverse.
Compute all the minors and cofactors of
1 2 3
2 0 1
2 3 4
(6.1) Find the values of a, b and c such the matrix below is skew symmetric.
0 0 d
0 2a − 3b + c 3a − 5b + 5c
2 0 5a − 8b + 6c
(6.2) Give an example of a skew symmetric matrix.
(6.3) Prove that A (4) 2 is symmetric whenever A is skewsymmetric.
(6.4) Determine an expression for det(A) in terms of det(A (T ) if A is a square skewsymmetric.
(6.5) Assume that A has an odd number of rows and also an odd number of columns. In this particular case, show that det(·) is an odd function
Consider the matrices A = −2 7 1
3 4 1
8 1 5 ,
B = 8 1 5
3 4 1
−2 7 1 ,
C = −2 7 1
3 4 1
2 −7 3 .
Find elementary matrices E1, E2 and E3 such that
(5.1) E1A = B,
(5.2) E1B = A,
(5.3) E2A = C,
(5.4) E3C = A.
Determine whether or not the following matrices are in row echelon form or not? (4.1)
(1 2 −2)
( 0 1 2)
( 0 0 1)
(4.2) (1 2 −2)
(0 1 2 )
( 0 0 1 )
Determine whether or not the following matrices are in row echelon form or not? ( 12-2 012 001) (12-2 012 001)
Compute all the minors is and cofactors of (123 201 234)
Consider the matrices
A = −2 7 1
3 4 1
8 1 5,
B =8 1 5
3 4 1
−2 7 1,
C = −2 7 1
3 4 1
2 −7 3
Find elementary matrices E1, E2 and E3 such that
(5.1) E1A = B,
(5.2) E1B = A,
(5.3) E2A = C,
(5.4) E3C = A.
Change the following equations in to augmented matrix
x-y+2z=1
3x-y+5z=-2
4x+2y+(x2-8)z=(x+2)
And determine values of x where:-
There is no solution
And where there is exactly one solution
And where there infinitely many solutions
