If A=[ 2 3 5 ] and B=[ 5 7 8 ], then the order of A B is (a) 1 ×1 (b

step 1 So in the given question what we have is we have a matrix A which is given as 2, 3, 5, 5, 5, 8.

If A=[ 2 3 5 ] and B=[ 5 7 8 ],...

If $A=\left[\begin{array}{l}2 \\ 3 \\ 5\end{array}\right]$ and $B=\left[\begin{array}{lll}5 & 7 & 8\end{array}\right]$, then the order of $A B$ is
(a) $1 \times 1$
(b) $3 \times 3$
(c) $3 \times 1$
(d) $1 \times 3$

Key Concepts

Outer Product

The outer product is a specific use of matrix multiplication where a column vector is multiplied by a row vector. This operation results in a matrix whose order is determined by the number of components in the column vector and the number of components in the row vector. It is a useful concept in various applications across linear algebra and related fields, such as in constructing matrices with specific patterns or in statistical applications.

Matrix Dimensions

The concept of matrix dimensions, also known as the order of a matrix, refers to the number of rows and columns in the matrix. This forms the basis for many operations in linear algebra, including matrix addition and multiplication. Understanding the dimensions is critical since operations like multiplication have requirements regarding compatibility of these dimensions.

Matrix Multiplication

Matrix multiplication involves combining two matrices in a way that the element at each position in the resulting matrix is computed as the dot product of a row from the first matrix and a column from the second matrix. A necessary condition for the multiplication to be defined is that the number of columns in the first matrix matches the number of rows in the second matrix. The dimensions of the resulting matrix are determined by the number of rows of the first matrix and the number of columns of the second matrix.

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