Skip to content
Education With Hamza
Log in
1st Year · Mathematics

Matrix Inverse Method | Class 11 Maths Ex 2.6 Q6 Help

Updated 2 min read

In short

Master the 3x3 Matrix Inverse Method. Step-by-step Urdu/Hindi guide for Class 11 Maths Ex 2.6, Q6. Solve linear equations easily with Hamza's tips.

On this page6 sections
  1. Detailed Methodology
  2. 1. Matrix Formation
  3. 2. The Determinant Check
  4. Finding the Adjoint of a 3x3 Matrix
  5. 3. Solving for X
  6. Special Case: Question 6 Part 4

Advertisement

Detailed Methodology

The Matrix Inverse Method (also known as the Inversion Method) is a powerful algebraic tool used to solve systems of linear equations. While students often learn this for 2x2 matrices in 9th grade, the 11th-grade curriculum (National Book Foundation) expands this to 3x3 systems, requiring a deep understanding of determinants, cofactors, and adjoints.

1. Matrix Formation

First, convert the system of linear equations into a matrix equation AX = B.

  • Matrix A: Contains the coefficients of variables (x, y, z).
  • Matrix X: The column matrix of variables [x, y, z].
  • Matrix B: The constants on the right side of the equations.

2. The Determinant Check

Calculate |A| by expanding along the first row (R1).

Important:

If |A| = 0, the matrix is singular, and the system has no solution. Do not proceed further.

Finding the Adjoint of a 3x3 Matrix

This is the most time-consuming part. Follow the Co-factor Method meticulously:

Calculate Minors

Find the determinant of the 2x2 matrix remaining after hiding the row and column of an element.

Apply Signs

Use the sign pattern:
+ - +
- + -
+ - +

Transpose Matrix

Swap the rows and columns of your co-factor matrix to finally get Adj(A).

Advertisement

3. Solving for X

Once you have the inverse matrix A-1 = Adj(A) / |A|, multiply it by Matrix B.

Operation Description
Scalar Division Raja Hamza Khan recommends dividing by the determinant (|A|) at the very last step to avoid working with messy fractions too early.
Row × Column Multiply the rows of A-1 by the single column of B.
Verification Always plug your final values (x, y, z) back into the original equations to check for accuracy.

Special Case: Question 6 Part 4

When variables appear in the denominator (e.g., 2/x + 3/y + 10/z = 4), Hamza explains a clever workaround:

Let 1/x = u
Let 1/y = v
Let 1/z = w

Solve for [u, v, w] as usual, then find the reciprocal of your answers to get the final values of [x, y, z].

  • #matrix inverse
  • #matrix method
  • #class 11
  • #qst year

Advertisement