matrix_solve_2x2

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description must fully disclose behavioral traits. It only states the method (Cramer's rule) and domain, but fails to describe critical behaviors: input format expectations (e.g., string arrays for numbers), error handling (e.g., singular matrices), output format, or computational constraints. This is inadequate for a tool with parameters and no output schema.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is extremely concise—a single sentence that efficiently conveys the core purpose, method, and domain/category. It is front-loaded with essential information and has no wasted words, making it easy to parse quickly.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the complexity (solving linear equations), lack of annotations, 0% schema coverage, and no output schema, the description is severely incomplete. It omits parameter details, behavioral context, usage guidelines, and output expectations, making it inadequate for an agent to use the tool correctly without guesswork.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must compensate by explaining parameters. It does not mention matrix_a or vector_b at all, nor their semantics (e.g., matrix_a as a 2x2 array, vector_b as a 2-element array), expected formats, or examples. This leaves both parameters undocumented, failing to add any meaning beyond the bare schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose: solving a 2x2 system of linear equations using Cramer's rule, with the domain and category specified. It uses specific verbs ('solve') and resources ('2x2 system of linear equations'), but does not explicitly differentiate from sibling tools like matrix_solve_3x3, which is a similar tool for 3x3 matrices.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category, but does not specify prerequisites, limitations (e.g., only for 2x2 matrices), or when to choose other tools like matrix_solve_3x3 or gaussian_elimination. This leaves the agent without clear usage context.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.