4 Create the following matrices with MATLAB and use them in

4. Create the following matrices (with MATLAB), and use them in the exercises that follow:

a. Create a row vector called d from the second column of matrix a.

b. Combine vector b and the transpose of vector d to create matrix e, a two-dimensional matrix with three rows and two columns.

c. Combine vector b and vector d to create matrix f, a one-dimensional matrix with six rows and one column.

d. Create a matrix g, with four rows and three columns, from matrix a and the first three elements of matrix c.

e. Create a column vector h with the first element equal to a_1,3, the second element equal to c_1,2, and the third element equal to b_2,1.

5. The action of sun sunlight on green plants powers a process called photosynthesis, in which plants capture energy from light and store energy in chemical form. During photosynthesis, x1 moles of carbon dioxide (CO₂) and x2 moles of water (H₂O) are converted into x3 moles of oxygen (O₂) and x4 moles of complex carbohydrates, such as glucose (C₆H₁₂O₆). Find the smallest positive integer solution that balances the chemical equation (with or without MATLAB)

x1 CO₂ + x2 H₂O ? x3 O₂ + x4 C₆H₁₂O₆

5 3 22 3 8 5 14 3 82

Solution

We want to create the following matrices (with MATLAB), and use them in the exercises that follow:

function createD()

A=[15 3 22;3 8 5;14 3 82]

for i=1:3

    D(i)=A(i,3);

end

D=D\';

D

End

Output:

>> createD()

A =

    15     3    22

     3     8     5

    14     3    82

D =

    22

     5

    82

b)

function createE()

B=[1; 5; 6]

D=[22; 5; 82]

E=[B D]

End

Output:

>>createE()

B =

     1

     5

     6

D =

    22

     5

    82

E =

     1    22

     5     5

     6    82

c)

function createF()

B=[1; 5; 6]

D=[22; 5; 82]

F=[B; D]

end

Output:

>>createF()

B =

     1

     5

     6

D =

    22

     5

    82

F =

     1

     5

     6

    22

     5

    82

d)

function createG()

A=[15 3 22;3 8 5;14 3 82]

for i=1:3

    D(i)=A(i,1);

end

D=D\';

for i=1:3

    E(i)=A(i,3);

end

E=E\';

B=[1; 5; 6]

C=[12 18 5];

C=C\';

C

G=[D E C]

end

Output:

>>createG()

A =

    15     3    22

    3     8     5

    14     3    82

B =

     1

     5

     6

C =

    12

    18

     5

G =

    15    22    12

     3     5    18

    14    82     5

e)

function createH()

A=[15 3 22;3 8 5;14 3 82]

for i=1:3

    D(i)=A(2,i);

end

D

C=[12 18 5];

for i=1:3

    E(i)=A(3,i);

end

E

B=[1; 5; 6];

B=B\';

B

H=[D; C; E; B]

end

Output:

>>createH()

A =

    15     3    22

     3     8     5

    14     3    82

D =

     3     8     5

E =

    14     3    82

B =

     1     5     6

H =

     3     8    5

    12    18     5

    14     3    82

     1     5     6

f)

function createK()

A=[15 3 22;3 8 5;14 3 82]

K=[A(1,1) A(1,3); A(3,1) A(3,3)]

end

Output:

>> createK()

A =

    15     3    22

     3     8     5

    14     3    82

K =

    15    22

    14    82