Solution:

• The variable for the given matrix A=[1432] is “A = [1 4; 3 2]”, and the output of the operation “3*A” is [31296].

• The variable for the given two matrices A=[1432] and C=[325412] are “A = [1 4; 3 2]” and “C = [3 2 5; 4 1 2]”. The output of the operation “A*C” is [1961317819].

• The variable for the given two matrices C=[325412] and B=[213156360] are “C = [3 2 5; 4 1 2]” and “B = [2 1 3; 1 5 6; 3 6 0]”. So the other multiplication is possible and the output of the operation “C*B” is [234321152118].

• The variable for the given matrix A=[1432] and perform the operation “3*A”.

The given matrices are,

A=[1432]

B=[213156360]

And,

C=[325412]

Substitute [1432] for A in the expression “3*A”.

3*A=3[1432]=[1×34×33×32×3]=[31296]

Therefore, the elements of the matrix “3*A” are [31296].

Now, verify the expression output through the MATLAB command.

MATLAB Code:

A = [1 4; 3 2]

% Define the command to get the matrix “A”.

3*A

% Define the command to get the output of the expression “3*A”.

Save the MATLAB script with name, chapter2_45251_2_42_1E.m in the current folder. Execute the script by typing the script name at the command window to create the variable for the given matrix A=[1432] and perform the operation “3*A”.

Result:

Therefore, the variable for the given matrix A=[1432] is “A = [1 4; 3 2]”, and the output of the operation “3*A” is [31296].

• The variable for the given two matrices A=[1432] and C=[325412] and perform the operation “A*C”.

The given matrices are,

A=[1432]

B=[213156360]

And,

C=[325412]

Substitute [1432] for A and substitute [325412] for C in the expression “A*C”.

A*C=[1432][325412]=[(1×3)+(4×4)(1×2)+(4×1)(1×5)+(4×2)(3×3)+(2×4)(3×2)+(2×1)(3×5)+(2×2)]=[1961317819]

Therefore, the elements of the matrix “A*C” are [1961317819].

Now, verify the expression output through the MATLAB command.

MATLAB Code:

A = [1 4; 3 2]

% Define the command to get the matrix “A”.

C = [3 2 5; 4 1 2]

% Define the command to get the matrix “C”.

A*C

% Define the command to get the output of the expression “A*C”.

Save the MATLAB script with name, chapter2_45251_2_42_2E.m in the current folder. Execute the script by typing the script name at the command window to create the variable for the given two matrices A=[1432] and C=[325412]. Perform the operation “A*C”.

Result:

Therefore, the variable for the given two matrices A=[1432] and C=[325412] are “A = [1 4; 3 2]” and “C = [3 2 5; 4 1 2]”. The output of the operation “A*C” is [1961317819].

• Whether other multiplication operation can be performed in part 2 or not.

The given matrices are,

A=[1432]

B=[213156360]

And,

C=[325412]

Substitute [213156360] for B and substitute [325412] for C in the expression “C*B”.

C*B=[325412][213156360]=[(3×2)+(2×1)+(5×3)(3×1)+(2×5)+(5×6)(3×3)+(2×6)+(5×0)(4×2)+(1×1)+(2×3)(4×1)+(1×5)+(2×6)(4×3)+(1×6)+(2×0)]=[234321152118]

Therefore, the elements of the matrix “C*B” are [234321152118].

Now, verify the expression output through the MATLAB command.

MATLAB Code:

C = [3 2 5; 4 1 2]

% Define the command to get the matrix “C”.

B = [2 1 3; 1 5 6; 3 6 0]

% Define the command to get the matrix “B”.

C*B

% Define the command to get the output of the expression “C*B”.

Save the MATLAB script with name, chapter2_45251_2_42_3E.m in the current folder. Execute the script by typing the script name at the command window to create the variable for the given two matrices C=[325412] and B=[213156360]. The other multiplication operation that can be performed are “C*B”.

Result:

Therefore, the variable for the given two matrices C=[325412] and B=[213156360] are “C = [3 2 5; 4 1 2]” and “B = [2 1 3; 1 5 6; 3 6 0]”. So the other multiplication is possible and the output of the operation “C*B” is [234321152118].