A retail analyst uses a matrix to track inventory across four warehouse zones, where each row represents one zone. To adjust for a storage error that double-counted the items in Zone 3 (represented by Row 3), the analyst applies the row operation ${}0.5R_3$. What does this notation specifically require the analyst to do?

The Non-Zero Constant Rule

A small business owner uses a matrix to track the costs of materials across different product lines. To adjust for inflation or bulk discounts, they must apply row operations. Match each matrix term or notation with its corresponding rule or definition.

A budget analyst is adjusting a matrix where each row represents a different department's monthly expenses. To account for a 5% increase in the maintenance department's budget (Row 2), the analyst applies the row operation ${}1.05R_2$. According to the rules of row operations, this means that every individual entry in Row 2 must be multiplied by 1.05.

Rules for Matrix Row Scaling