Matrix Operations Quiz

A square matrix where all diagonal elements are the same, and all other elements are zero.

A matrix with at least one non-zero element.

A type of scalar matrix where all diagonal elements are set to 1.

Two matrices with the same dimensions (rows and columns).

The operation of adding or subtracting corresponding elements of two comparable matrices.

The order of addition does not affect the result. A + B = B + A.

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Each element in the matrix has a specific position defined by its row and column index.

The order of a matrix is defined by the number of rows (m) and columns (n) it has, expressed as m x n. For example, a matrix with 3 rows and 2 columns has an order of 3 x 2.

Two matrices are equal if they have the same order (same number of rows and columns) and all corresponding elements are equal. For example, if both matrices have 2 rows and 2 columns, you need to compare each position (a11, a12, a21, a22) and ensure they match.

A square matrix is a matrix with an equal number of rows and columns (m = n). For instance, a 3x3 matrix is a square matrix because it has 3 rows and 3 columns.

A column matrix consists of only a single column. For instance, a 4x1 matrix is a column matrix because it has 4 rows and just 1 column.

A row matrix consists of only a single row. For instance, a 1x3 matrix is a row matrix because it has just 1 row and 3 columns.

Null matrix is a matrix where all the elements are zero. It's also known as a zero matrix. Regardless of its size, all elements need to be zero for it to be considered a null matrix.

A diagonal matrix is where only the diagonal elements (top left to bottom right) are non-zero. Rest of the elements in a diagonal matrix are zero. They are always square matrices.

Adding matrices in groups does not change the result. For example, (A + B) + C = A + (B + C).

Adding the zero matrix to any matrix results in the original matrix. A + 0 = A.

Multiplying a matrix by a scalar k means multiplying each element of the matrix by k. For example, kA = k × [each element of A]

Adding the negative of a matrix to itself results in the zero matrix. A + (-A) = 0

Multiplying a matrix by a scalar k and then adding it to another matrix multiplied by scalar k is the same as multiplying the sum of the matrices by k. k(A + B) = kA + kB

Multiplying a matrix by a sum of scalars is the same as multiplying the matrix by each scalar separately and then adding the results. (k1 + k2)A = k1A + k2A

The product of two matrices is defined only if the number of columns in the first matrix equals the number of rows in the second matrix. The product is itself a matrix.

A method of multiplying two matrices, where the resulting matrix has elements that are the dot product of rows from the first matrix and columns from the second matrix.

A matrix with only one column, representing a set of values. Often used to represent prices, quantities, or other related data.

When a column matrix representing prices is multiplied by a row matrix representing quantities, the result is a single value representing the total cost.

A matrix that represents the prices of different items in a shop.

A matrix that represents the quantities of items a person wants to buy.

The process of calculating the total cost of items by multiplying the prices with the quantities and summing up the results.

In the context of matrix multiplication, a single row matrix representing the number of items a person intends to buy.

The element at the i-th row and j-th column of a matrix is represented by the symbol a_{ij}.

The ability of two matrices to be multiplied together is determined by their dimensions. Specifically, the number of columns in the first matrix must equal the number of rows in the second matrix.

Matrix multiplication is not commutative, meaning AB ≠ BA. The order of the matrices matters.

The result of multiplying two matrices is a new matrix with a number of rows equal to the number of rows in the first matrix and a number of columns equal to the number of columns in the second matrix.

The elements of the product matrix represent the total cost of a specific item (from a specific store).

The order of the matrices in a multiplication affects the resulting product matrix. It's not always commutative; AB ≠ BA.

A matrix where all elements are zero. It is the additive identity element for matrix addition, meaning adding it to any matrix results in the original matrix.

A way to represent a collection of data in a rectangular array, organized in rows and columns.

The result of multiplying a matrix by a column matrix, where each element of the resulting vector is obtained by multiplying the corresponding elements of the matrix row and column vector and summing the results.

Representing the price of different products in a row vector and the quantity of each product purchased in a column vector.

Representing the products purchased by different people in a matrix, with each row representing a person's purchases.

A mathematical representation of multiplying a matrix by a column vector using symbolic variables instead of specific numbers.

The first element of the resulting vector is obtained by multiplying the elements of the first row of the matrix by corresponding elements of the column vector and summing the results.

Each element in the resulting vector is calculated by multiplying the corresponding elements of a matrix row and the column vector and summing the results.

The entire multiplication process is a summation of products where each product involves an element of the matrix row and the corresponding element of the column vector.

The final result of multiplying a matrix by a column vector is another column vector.

The elements of the resulting vector are generated using a consistent rule: multiplying the elements of each row of the matrix by the respective elements of the column vector and summing the results.