6 - Matrices Flashcards
(2) (4)
(3) + (2)
(4) (7)
(6)
(5)
(11)
(2 3)(4 5)
(6 2)
(26 16)
Draw a 4 x 5 matrix
Why is this not possible:
(2) (2 3 4)
(3) (3 4 5)
Rows not equal to columns.
Draw the I2 matrix
(1 0)
(0 1)
What is the determinant of:
(a b)
(c d)
ad-bc
What is a singular matrix?
A matrix with det = 0 and no inverse.
What is the determinant of:
(a b c)
(d e f)
(g h i)
a(e f) - b(d f) + c(d e)
(h i) (g i) (g h)
What is a minor of a 3x3 matrix?
The determinant of thee 2x2 matrix remaining after the row and column containing a specific element has been crossed out.
What is the inverse of matrix M?
M^-1 such that MM^-1 = M^-1M = I.
What is the inverse of:
(a b)
(c d)
1/detM(d -b)
(-c a)
What is (AB)^-1 if they are both non-singular?
b^-1A^-1.
How do you transpose a matrix?
Interchange the rows and columns.
How do you invert a 3x3 matrix?
.Find the determinant.
.Form a matrix of minors.
.Form a matrix of cofactors.
.Transpose the matrix of cofactors.
.The inverse is 1/det C^T.
If a(x) = v, what is (x)
(y) (y)
(z) (z)
A^-1v.
Define consistent.
There is at least one set of values which satisfies all the equations simultaneously.
What does it mean when the planes meet at a point?
Consistent, one solution, non-singular.
What does it mean when the planes form a sheaf?
Consistent, infinitely many solutions, singular.
What does it mean when the planes form a prism?
Inconsistent, no solutions, singular.
What does it mean when two or more planes are parallel and non-identical?
Inconsistent, no solutions.
What does it mean when all solutions represent the same plane?
Consistent, infinitely many solutions.
How do you know if the planes are parallel?
If one row is a linear multiple of another row.
