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Question 2
*
1 point
Consider two matrices 
A and 
B. What is the order of the Matrix 
AB ?

A=([1,-2],[0,1],[2,3]),B=([4,-1],[3,1])

3×3

2×2

2×3

3×2

Question 22\newline*\newline11 point\newlineConsider two matrices A \mathrm{A} and B \mathrm{B} . What is the order of the Matrix AB A B ?\newlineA=(120123),B=(4131) A=\left(\begin{array}{cc} 1 & -2 \\ 0 & 1 \\ 2 & 3 \end{array}\right), B=\left(\begin{array}{cc} 4 & -1 \\ 3 & 1 \end{array}\right) \newline3×3 3 \times 3 \newline2×2 2 \times 2 \newline2×3 2 \times 3 \newline3×2 3 \times 2

Full solution

Q. Question 22\newline*\newline11 point\newlineConsider two matrices A \mathrm{A} and B \mathrm{B} . What is the order of the Matrix AB A B ?\newlineA=(120123),B=(4131) A=\left(\begin{array}{cc} 1 & -2 \\ 0 & 1 \\ 2 & 3 \end{array}\right), B=\left(\begin{array}{cc} 4 & -1 \\ 3 & 1 \end{array}\right) \newline3×3 3 \times 3 \newline2×2 2 \times 2 \newline2×3 2 \times 3 \newline3×2 3 \times 2
  1. Matrix A Order: Matrix A has 33 rows and 22 columns, so its order is 3×23\times2.
  2. Matrix B Order: Matrix B has 22 rows and 22 columns, so its order is 2×22\times2.
  3. Matrix Multiplication Condition: To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. Since AA is 3×23\times2 and BB is 2×22\times2, we can multiply them.
  4. Resulting Matrix Order: The order of the resulting matrix ABAB will have the same number of rows as matrix AA and the same number of columns as matrix BB. So, the order of ABAB will be 3×23\times2.

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