Question

Given a matrix F = [3 6 7] [0 2 1] [2 3 4]. Use Cramer’s rule to find the inverse matrix of F.

Given a matrix G = [1 2 4] [0 -3 1] [0 0 3]. Use Cramer’s rule to find the inverse matrix of G.

Given a matrix H = [3 0 0] [-1 1 0] [-2 3 2]. Use Cramer’s rule to find the inverse matrix of H.

Answer #1

Using cramer's method find the inverse of the matrix.

Given F(2) = 1, F'(2) = 7, F(4) = 3, F′(4) = 7
and G (4) = 2 , G′(4)= 6, G(3)= 4, G′(3)=11,
find the following.
(a) H(4) if H(x) = F(G(x))
H(4) =
(b) H′(4) if H(x) = F(G(x))
H′(4) =
(c) H(4) if H(x) = G(F(x))
H(4) =
(d) H′(4) if H(x) = G(F(x))
H'(4)=

3) If A = 3
1 and B
= 1 7
0
-2
5 -1
Find
a) BA
b) determinant
B
c) Adjoint A
d)
A-1
4) Using matrix method solve the following simultaneous
equations
5x – 3y = 1
2x – 2y = -2
5) Given that f(x) = 6x - 5 g(x) = 3x +
4 and h(x) = 4x – 6
2
Find:-
i)...

Use Cramer’s Rule to solve the equations :
? − ? + 2? = −3
4 = ?3 + ?2 + ?
3− = ? + ? + ?2

Find the inverse matrix of
[ 3 2 3 1 ]
[ 2 1 0 0 ]
[ 3 -5 1 0 ]
[ 4 2 3 1 ]
This is all one 4x4 matrix
Required first step add second row multiplied by (-1) to first
row
try to not use fractions at all to solve this problem

LINEAR ALGEBRA
For the matrix B=
1 -4 7 -5
0 1 -4 3
2 -6 6 -4
Find all x in R^4 that are mapped into the zero vector by the
transformation Bx.
Does the vector:
1
0
2
belong to the range of T? If it does, what is the pre-image of
this vector?

Suppose f(1) = −1, f(2) = 0, g(1) = 2, g(2) = 7, and f 0 (1) =
1, f0 (2) = 4, g0 (1) = 8, g0 (2) = −4.
(a) Suppose h(x) = f(x^2 g(x)). Find h 0 (1).
(b) Suppose j(x) = f(x) sin(x − 1). Find j 0 (1).
(c) Suppose m(x) = ln(x)+arctan(x) e x+g(2x) . Find m0 (1).

Matrix A= -2 1 0
2 -3 4
5 -6 7
vector u= 1
2
1
a) Is the vector u in Null(A) Explain in detail why
b) Is the vectro u in Col( A) Explain in detail why

Find the LU factorization of the matrix
a)
( 6 2 0
-12 -3 -3
-6 -1 -14
9 -12 45 )
b) ( 2 -1 -2 4
6 -8 -7 12
4 -22 -8 14 )

Matrix A is given as A =
0 2 −1
−1 3 −1
−2 4 −1
a) Find all eigenvalues of A.
b) Find a basis for each eigenspace of A.
c) Determine whether A is diagonalizable. If it is, ﬁnd an
invertible matrix P and a diagonal matrix D such that D =
P^−1AP.
Please show all work and steps clearly please so I can follow
your logic and learn to solve similar ones myself. I...

#2. For the matrix A = 1 2 1 2 3 7 4 7 9 find the
following. (a) The null space N (A) and a basis for N (A). (b) The
range space R(AT ) and a basis for R(AT )
. #3. Consider the vectors −→x = k − 6 2k 1 and −→y =
2k 3 4 . Find the number k such that the vectors...

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