Matrix multiplication (*) in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this matrix multiplication?

Consider the following MATLAB code multiplying two matrices. What is the resulting matrix?

MATLAB

A = [1 2; 3 4];
B = [5 6; 7 8];
C = A * B;
disp(C);

A [12 16; 28 40]

B [19 22; 43 50]

C [5 12; 21 32]

D [17 20; 39 46]

💡 Hint

Remember matrix multiplication sums the products of rows of the first matrix with columns of the second.

Matrix multiplication multiplies rows of A by columns of B. For example, element (1,1) is 1*5 + 2*7 = 19.

❓ Predict Output

intermediate

What error does this matrix multiplication code produce?

What error will this MATLAB code produce when run?

MATLAB

A = [1 2 3; 4 5 6];
B = [7 8; 9 10];
C = A * B;

A Error: Undefined function or variable 'B'.

B No error, output is a 2x2 matrix.

C Error: Matrix dimensions must be square.

D Error: Inner matrix dimensions must agree.

💡 Hint

Check the number of columns in A and rows in B for multiplication compatibility.

Matrix multiplication requires the number of columns in A to equal the number of rows in B. Here, A is 2x3 and B is 2x2, so multiplication is invalid.

❓ Predict Output

advanced

What is the output of multiplying a matrix by identity matrix?

Given the code below, what is the output matrix C?

MATLAB

A = [3 4; 1 2];
I = eye(2);
C = A * I;
disp(C);

A [3 4; 1 2]

B [1 0; 0 1]

C [4 3; 2 1]

D [0 0; 0 0]

💡 Hint

Multiplying by the identity matrix should not change the original matrix.

The identity matrix acts like 1 in multiplication, so A * I = A.

❓ Predict Output

advanced

What is the output of this matrix multiplication with a transpose?

What is the output of the following MATLAB code?

MATLAB

A = [1 2 3];
B = [4; 5; 6];
C = A * B;
disp(C);

A 32

B [4 5 6; 8 10 12]

C [1 2 3; 4 5 6]

D Error: Inner matrix dimensions must agree.

💡 Hint

Check the dimensions of A and B before multiplication.

A is 1x3 and B is 3x1, so multiplication results in a 1x1 scalar: 1*4 + 2*5 + 3*6 = 32.

🧠 Conceptual

expert

How many elements does the resulting matrix have after multiplication?

If matrix A is 4x3 and matrix B is 3x5, how many elements will the matrix C = A * B have?

A 15

B 12

C 20

D 7

💡 Hint

The resulting matrix size is rows of A by columns of B.

Multiplying a 4x3 by a 3x5 matrix results in a 4x5 matrix, which has 4*5=20 elements.