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Business Mathematics and Basic Statistics · Class 12 Commerce

Ch 11Determinants and Cramer's Rule — Class 12 Business Mathematics and Basic Statistics, concept-first.

This WBCHSE Class 12 Commerce Business Mathematics and Basic Statistics chapter builds directly on the previous chapter's matrices to introduce the determinant — a single number computed from a square matrix — and then uses it to solve a system of two linear equations in two unknowns by Cramer's Rule, a systematic alte…

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Key concepts

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Determinant of a 2×2 Matrix

For , the determinant — the product of the leading diagonal minus the product of the other diagonal. A determinant of 0 signals the matrix's rows/columns are proportional; a nonzero determinant is what guarantees a linea…

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Chapter contents

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1

The Determinant of a 2×2 Matrix

This WBCHSE Class 12 Commerce Business Mathematics and Basic Statistics chapter builds directly on the previous chapter's matrices to introduce the determinant — a single number computed from a square…

2

Setting Up Cramer's Rule — the Determinants D, Dₓ and D_y

This chapter uses determinants to solve a system of two linear equations in two unknowns, and :

3

Solving a Two-Variable System by Cramer's Rule

Once , and are found, and provided , the solution of the system is

Exercises

+Show 3 questions3 questions
  1. Q8Evaluate the determinant $\begin{vmatrix}-5&3\\4&-2\end{vmatrix}$.Free
  2. Q9Using Cramer's Rule, solve $2x-y=5$ and $x+3y=6$.Preview
  3. Q10A sum of ₹5,000 is divided between two people such that twice the first person's share exceeds the second person's share by ₹1,000. Using Cr…Preview

More questions

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  1. Example 1Evaluate the determinant of $A=\begin{pmatrix}4&3\\2&5\end{pmatrix}$.Free
  2. Example 2Evaluate $\begin{vmatrix}6&-2\\-3&4\end{vmatrix}$.Free
  3. Example 3Find the value(s) of $x$ for which $\begin{vmatrix}x&3\\2&x-1\end{vmatrix}=0$.Free
  4. Example 4Using Cramer's Rule, solve the system of equations $2x+y=7$ and $x-y=2$.Preview
  5. Example 5Using Cramer's Rule, solve the system of equations $3x+2y=4$ and $x-3y=5$.Preview
  6. Example 6The total cost of 3 notebooks and 2 pens is ₹78, while the total cost of 5 notebooks and 4 pens is ₹138. Using Cramer's Rule, find the cost…Preview
  7. Example 7Verify, by substitution, that $x=2,y=-1$ is indeed the solution of the system $3x+2y=4$, $x-3y=5$ (solved by Cramer's Rule in an earlier Wor…Preview