Educational

In a parliament election, a political party hired a public relations firm to promote its candidates in three ways – telephone, house calls and letters. The cost per contact (in paisa) is given in matrix A as The number of contacts of each type made in two cities X and Y is given in the matrix B as Find the total amount spent by the party in the two cities. What should one consider before casting his/her vote – party’s promotional activity or their social activities?

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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 \[ […]

In a parliament election, a political party hired a public relations firm to promote its candidates in three ways – telephone, house calls and letters. The cost per contact (in paisa) is given in matrix A as The number of contacts of each type made in two cities X and Y is given in the matrix B as Find the total amount spent by the party in the two cities. What should one consider before casting his/her vote – party’s promotional activity or their social activities? Read More »

There are 2 families A and B. There are 4 men, 6 women and 2 children in family A, and 2 men, 2 women and 4 children in family B. The recommend daily amount of calories is 2400 for men, 1900 for women, 1800 for children and 45 grants of proteins for men, 55 grams for women and 33 grams for children. Represent the above information using matrix. Using matrix multiplication, calculate the total requirement of calories and proteins for each of the two families. What awareness can you create among people about the planned diet from this question ?

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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

There are 2 families A and B. There are 4 men, 6 women and 2 children in family A, and 2 men, 2 women and 4 children in family B. The recommend daily amount of calories is 2400 for men, 1900 for women, 1800 for children and 45 grants of proteins for men, 55 grams for women and 33 grams for children. Represent the above information using matrix. Using matrix multiplication, calculate the total requirement of calories and proteins for each of the two families. What awareness can you create among people about the planned diet from this question ? Read More »

To promote making of toilets for women, an organisation tried to generate awareness through (i) house calls (ii) letters, and (iii) announcements. The cost for each mode per attempt is given below: (i) ₹50 (ii) ₹20 (iii) ₹40 The number of attempts made in three village X, Y and Z are given below: Find the total cost incurred by the organisation for three villages separately, using matrices.

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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

To promote making of toilets for women, an organisation tried to generate awareness through (i) house calls (ii) letters, and (iii) announcements. The cost for each mode per attempt is given below: (i) ₹50 (ii) ₹20 (iii) ₹40 The number of attempts made in three village X, Y and Z are given below: Find the total cost incurred by the organisation for three villages separately, using matrices. Read More »

A trust fund has ₹30000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using the trust fund must obtain an annual total interest of (i) ₹1800 (ii) ₹2000.

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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

A trust fund has ₹30000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using the trust fund must obtain an annual total interest of (i) ₹1800 (ii) ₹2000. Read More »

In a legislative assembly election, a political group hired a public relations firm to promote its candidates in three ways: telephone, house calls and letters. The cost per contact (in paise) is given matrix A as A=Cost per contact [[40] – Telephone, [100]-House call, [50]-Letter] The number of contacts of each type made in two cities X and Y is given in matrix B as Find the total amount spend by the group in the two cities X and Y.

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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 \[

In a legislative assembly election, a political group hired a public relations firm to promote its candidates in three ways: telephone, house calls and letters. The cost per contact (in paise) is given matrix A as A=Cost per contact [[40] – Telephone, [100]-House call, [50]-Letter] The number of contacts of each type made in two cities X and Y is given in matrix B as Find the total amount spend by the group in the two cities X and Y. Read More »

The cooperative stores of a particular school 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 each respectively. Find the total amount the store will receive from selling all the items.

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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}

The cooperative stores of a particular school 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 each respectively. Find the total amount the store will receive from selling all the items. Read More »

Three shopkeepers A, B and C go to a store by stationary. A purchases 12 dozen notebooks, 5 dozen pens and 6 dozen pencils. B purchases 10 dozen notebooks, 6 dozen pens and 7 dozen pencils. C purchases 11 dozen notebooks, 13 dozen pend and 8 dozen pencils. A notebook costs 40 paise, a pen costs ₹1.25 and a pencil costs 35 paise. Use matrix multiplication to calculate each individual’s bill.

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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 &

Three shopkeepers A, B and C go to a store by stationary. A purchases 12 dozen notebooks, 5 dozen pens and 6 dozen pencils. B purchases 10 dozen notebooks, 6 dozen pens and 7 dozen pencils. C purchases 11 dozen notebooks, 13 dozen pend and 8 dozen pencils. A notebook costs 40 paise, a pen costs ₹1.25 and a pencil costs 35 paise. Use matrix multiplication to calculate each individual’s bill. Read More »

Let A = [[1, 1, 1], [3, 3, 3]], B = [[3, 1], [5, 2], [-2, 4]] and C = [[4, 2], [-3, 5], [5, 0]] Verify that AB = AC though B ≠ C, A ≠ O.

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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

Let A = [[1, 1, 1], [3, 3, 3]], B = [[3, 1], [5, 2], [-2, 4]] and C = [[4, 2], [-3, 5], [5, 0]] Verify that AB = AC though B ≠ C, A ≠ O. Read More »

If A and B are square matrices of the same order such that AB = BA, then show that (A + B)^2 = A^2 + 2AB + B^2

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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 +

If A and B are square matrices of the same order such that AB = BA, then show that (A + B)^2 = A^2 + 2AB + B^2 Read More »

Let A and B be square matrices of the other 3×3. Is (AB)^2 = A^2 B^2 ? Give reasons.

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Is (AB)² = A²B²? Question Let \(A\) and \(B\) be square matrices of order \(3 \times 3\). Is \[ (AB)^2 = A^2 B^2? \] Give reasons. Solution Step 1: Expand LHS \[ (AB)^2 = (AB)(AB) \] \[ = A(BA)B \] Step 2: Compare with RHS \[ A^2 B^2 = AABB \] Step 3: Key Observation

Let A and B be square matrices of the other 3×3. Is (AB)^2 = A^2 B^2 ? Give reasons. Read More »