Question

The first entry in the product Ax is a sum of products. Choose the correct answer below.

A. True. The first entry is a sum of products.
B. False. The first entry is a single product.
C. True. The first entry is a difference of products.
D. False. The first entry is a division of products.

Answer 1

The statement "The first entry in the product Ax is a sum of products" is true. Because the first entry in the product Ax is a sum of products (Option A).

Step-by-step explanation:

When you multiply a matrix, A, by a vector, x, the first entry in the product Ax is typically the sum of the products of the corresponding entries from the first row of A and the vector x. Therefore, the first entry in the product Ax is a sum of products is true.

To express this operation algebraically, if A has a first row represented by a₁₁, a₁₂, ..., a₁ₙ and the vector x is represented by x₁, x₂, ..., xₙ, then the first entry of Aₓ would be a₁₁x₁ + a₁₂x₂ + ... + a₁ₙxₙ.

Thus, the correct answer is A. True, the first entry in the product Ax is a sum of products.

Answer 2

The correct answer is True. The first entry in the product Ax is a sum of products, as it is obtained by multiplying each element of the first row of matrix A by the corresponding element in vector x and summing the results.

Step-by-step explanation:

The provided statement 'The first entry in the product Ax is a sum of products' refers to matrix multiplication. When multiplying a matrix A by a vector x, the first entry in the resulting vector is indeed a sum of products. Each element of the first row of matrix A is multiplied by the corresponding element in vector x, and those products are then added together to form the first entry of the product Ax.

To illustrate, consider a matrix A with a first row consisting of elements a1, a2, ..., an and a vector x with elements x1, x2, ..., xn. The first entry of the product Ax would be (a1 * x1) + (a2 * x2) + ... + (an * xn).