April 2026

Income Expenditure Matrix Problem Question The monthly incomes of Aryan and Babbar are in the ratio \(3:4\) and their expenditures are in the ratio \(5:7\). Each saves ₹15000 per month. Find their monthly incomes using matrix method. Solution Step 1: Assume \[ \text{Income} = 3x,\ 4x \] \[ \text{Expenditure} = 5y,\ 7y \] Step 2: […]

Election Campaign Cost using Matrix Question Cost per contact (in paise): \[ A = \begin{bmatrix} 140 \\ 200 \\ 150 \end{bmatrix} \] Number of contacts: \[ B = \begin{bmatrix} 1000 & 500 & 5000 \\ 3000 & 1000 & 10000 \end{bmatrix} \] Find total cost in cities \(X\) and \(Y\). Solution Step 1: Multiply \[

Nutrition Requirement using Matrix Question Two families A and B have men, women and children. Using matrix multiplication, find total calorie and protein requirements. Solution Step 1: Family Matrix \[ F = \begin{bmatrix} 4 & 6 & 2 \\ 2 & 2 & 4 \end{bmatrix} \] Step 2: Nutrition Matrix \[ N = \begin{bmatrix} 2400

Awareness Campaign Cost using Matrix Question Cost per attempt: \[ \text{House call} = 50,\quad \text{Letter} = 20,\quad \text{Announcement} = 40 \] Number of attempts: \[ \begin{aligned} X &: (400, 300, 100) \\ Y &: (300, 250, 75) \\ Z &: (500, 400, 150) \end{aligned} \] Solution Step 1: Form Matrices \[ A = \begin{bmatrix} 400

Investment Problem Using Matrix Question A trust fund of ₹30000 is invested in two bonds: 5% and 7%. Find the investment in each bond if total annual interest is: (i) ₹1800 (ii) ₹2000 Solution Step 1: Let Variables \[ x = \text{amount at 5%}, \quad y = \text{amount at 7%} \] Step 2: Form Equations

Election Campaign Cost using Matrix Question Cost per contact (in paise): \[ A = \begin{bmatrix} 40 \\ 100 \\ 50 \end{bmatrix} \] Number of contacts: \[ B = \begin{bmatrix} 1000 & 500 & 5000 \\ 3000 & 1000 & 10000 \end{bmatrix} \] Find total cost in cities \(X\) and \(Y\). Solution Step 1: Multiply \[

Matrix Word Problem – Total Sales Question A cooperative store has 10 dozen physics books, 8 dozen chemistry books and 5 dozen mathematics books. Their selling prices are ₹8.30, ₹3.45 and ₹4.50 respectively. Find the total amount received using matrix method. Solution Step 1: Convert to Matrix Form Quantity (in dozens): \[ Q = \begin{bmatrix}

Matrix Word Problem – Shopkeepers Bill Question Three shopkeepers A, B and C purchase notebooks, pens and pencils. Use matrix multiplication to calculate their bills. Solution Step 1: Convert into Matrices Quantity Matrix (in dozens): \[ Q = \begin{bmatrix} 12 & 5 & 6 \\ 10 & 6 & 7 \\ 11 & 13 &

Verify AB = AC Question Let \[ A = \begin{bmatrix} 1 & 1 & 1 \\ 3 & 3 & 3 \end{bmatrix},\ B = \begin{bmatrix} 3 & 1 \\ 5 & 2 \\ -2 & 4 \end{bmatrix},\ C = \begin{bmatrix} 4 & 2 \\ -3 & 5 \\ 5 & 0 \end{bmatrix} \] Verify that

Prove (A+B)² = A² + 2AB + B² Question If \(A\) and \(B\) are square matrices such that \(AB = BA\), prove that \[ (A + B)^2 = A^2 + 2AB + B^2. \] Solution Step 1: Expand \[ (A + B)^2 = (A + B)(A + B) \] \[ = A^2 + AB +