Example Question - matrix dimensions
Here are examples of questions we've helped users solve.
Matrix Arrangement Explanation
ترتيب المصفوفة يعطى بعدد الصفوف متبوعاً بعدد الأعمدة. في الصورة المرفقة، المصفوفة لها عدد صفوف هو 2 (اثنين) وعدد أعمدة هو 3 (ثلاثة). لذا ترتيب المصفوفة هو: 3 × 2 وبذلك تكون الإجابة هي الخيار ب) 3 × 2.
Understanding Square Matrices
A square matrix is a matrix that has the same number of rows and columns. We can determine if a matrix is square by checking their dimensions. Let's look at the matrices one by one: Matrix A: \[\begin{bmatrix} -1 & 4 & -2 \\ -4 & 3 & 5 \\ -3 & 1 & 6 \end{bmatrix}\] Matrix A has 3 rows and 3 columns, so it is a 3x3 matrix. Matrix B: \[\begin{bmatrix} 5 & 2 & -1 \\ 1 & 3 & 4 \\ \end{bmatrix}\] Matrix B has 2 rows and 3 columns, so it is a 2x3 matrix and not square. Matrix C: \[\begin{bmatrix} 12 & 6 \\ 5 & 3 \\ 0 & 7 \\ \end{bmatrix}\] Matrix C has 3 rows and 2 columns, so it is a 3x2 matrix and not square. Only Matrix A is a square matrix because it has the same number of rows and columns (3x3).
Matrix Multiplication Rules
For matrix multiplication to be possible, the number of columns in the first matrix must equal the number of rows in the second matrix. Matrix A is a 3x3 matrix, which means it has 3 rows and 3 columns. Matrix B is a 4x3 matrix, which means it has 4 rows and 3 columns. To multiply AB, the number of columns in A must equal the number of rows in B. Since A has 3 columns and B has 4 rows, AB cannot be calculated. To multiply BA, the number of columns in B must equal the number of rows in A. Since B has 3 columns and A has 3 rows, BA can be calculated. So, the correct answer is: B. only BA
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com