The Determinant

The Determinant

What is it?

Write i j k on top. Compute the three cofactors. Watch the minus in front of j. Practice one fully written expansion.

In simple words

• Write i j k on top.
• i (a2b3-a3b2)
• - j (a1b3-a3b1)
• State the rule, show the working, and check the answer.

Important terms

THE DETERMINANT: Write i j k on top. Compute the three cofactors. Watch the minus in front of j. Practice one fully written expansion.

THE DETERMINANT: Write i j k on top.

What you should learn

• State the rule or meaning of the determinant in easy words.
• Apply the determinant in a clear step-by-step solution.
• Check the conditions, working, and final answer for accuracy.

Examples

• i (a2b3-a3b2)
• - j (a1b3-a3b1)
• k (a1b2-a2b1)

MAIN IDEA

Write i j k on top. Compute the three cofactors. Watch the minus in front of j. Practice one fully written expansion.

EXAM USE

Write the rule first: Write i j k on top. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

Full school-level explanation

Write i j k on top. Compute the three cofactors. Watch the minus in front of j. Practice one fully written expansion.

Understand the idea, then apply it:

WHAT — THE DETERMINANT

Write i j k on top. Compute the three cofactors. Watch the minus in front of j. Practice one fully written expansion.

WHY — Why it matters

This rule is a separate learning unit inside cross product in components. It can be defined, applied, and checked in its own FBISE question.

HOW — How to answer

Write the rule first: Write i j k on top. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

MAIN IDEA

Write i j k on top. Compute the three cofactors. Watch the minus in front of j. Practice one fully written expansion.

Remember

• minus on j

Examples

• i (a2b3-a3b2)
• - j (a1b3-a3b1)
• k (a1b2-a2b1)

EXAM USE

Write the rule first: Write i j k on top. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.

Remember

• focused answer
• accurate support

Examples

• State the central idea
• Use one accurate detail
• Check the final response

How to answer a the determinant question

How it works

• Read the exact command word and identify what the question asks.
• State the matching idea, rule, or meaning before adding detail.
• Use the unit evidence or mathematical working that directly supports the answer.
• Check accuracy, relevance, and answer length before finishing.

Remember

• minus on j
• ijk determinant mnemonic
• middle component has a minus
• one minus on j
• minus on j
• focused answer
• accurate support
• minus on j

Deeper understanding

Go beyond memorising The Determinant. Connect the definition to reasons, relationships, exceptions, and exam wording.

Common mistakes

Exam focus

Core Idea

What to Know

Example or Evidence

How to Answer

Exam focus

Quick revision

• minus on j
• ijk determinant mnemonic
• middle component has a minus
• one minus on j
• THE DETERMINANT: Write i j k on top. Compute the three cofactors. Watch the minus in front of j. Practice one fully w
• THE DETERMINANT: Write i j k on top.

The j-component formula already includes the minus from the cofactor. Do not minus twice.

For long answers on The Determinant: define clearly → explain the main parts → give one example → state one exam caution.