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11th Business Maths Weekly Test - 2 ( Matrices and Determinants )

MABS Institution

11th Business Maths Weekly Test - 2 ( Matrices and Determinants )-Aug 2020

Time : 1.30 Hours

Part - A

Generic 2 - Answer All Question

Find the values of x if \(\begin{vmatrix} 2 & 4 \\5 & 1 \end{vmatrix}=\begin{vmatrix} 2x & 4\\6 & x \end{vmatrix}.\)

The technology matrix of an economic system of two industries is\(\begin{bmatrix} 0.6 & 0.9 \\ 0.20 & 0.80 \end{bmatrix}\) .Test whether the system is viable as per Hawkins-Simon conditions.

The technology matrix of an economic system of two industries is\(\begin{bmatrix} 0.50 & 0.30 \\ 0.41 & 0.33 \end{bmatrix}\). Test whether the system is viable as per Hawkins Simon conditions.

Show that \(\left[ \begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix} \right] \)is a singular matrix.

Suppose the inter-industry flow of the product of two sectors X and Yare given as under.

Production Sector Consumption Sector Domestic demand Gross output

X Y

X 15 10 10 35

Y 20 30 15 65

Find the gross output when the domestic demand changes to 12 for X and 18 for Y.

The technology matrix of an economic system of two industries is \(\begin{bmatrix} 0.50 & 0.25 \\ 0.40 & 0.67 \end{bmatrix}\). Test whether the system is viable as per Hawkins-Simon conditions.

Show that\(\left| \overset { x }{ 2x\underset { a }{ + } 2a } \quad \overset { y }{ 2y\underset { b }{ + } 2b } \quad \overset { z }{ 2z\underset { c }{ + } 2c } \right| =0\)

Using the property of determinants show that \(\begin{vmatrix} x &a &x+a \\ y & b &y+b \\z & c & z+c \end{vmatrix}=0.\)

Using the property of determinant, evaluate \(\begin{vmatrix} 6 &5 &12 \\ 2 & 4 &4 \\2 & 1 & 4 \end{vmatrix}.\)

Evaluate:\(\left| \begin{matrix} x & x+1 \\ x-1 & x \end{matrix} \right| \)

Part - B

Generic 5 - Answer All Question

Weekly expenditure in an office for three weeks is given as follows. Assuming that the salary in all the three weeks of different categories of staff did not vary, calculate the salary for each type of staff, using matrix inversion method.

Week Number of employees Total weekly
Salary (in rupees)

A B C

1^st week 4 2 3 4900

2^nd week 3 3 2 4500

3^rd week 4 3 4 5800

If \(A=\left[ \begin{matrix} 2 & 3 \\ 1 & 2 \end{matrix} \right] \)satisfies the equation A² kA +I₂ - + 2 = then, find k and also A^-1.

Let a, b and c denote the sides BC, CA and AB repectively of \(\Delta\) ABC. If \(\left| \begin{matrix} 1 & a & b \\ 1 & c & a \\ 1 & b & c \end{matrix} \right| =0\), then find the value of sin² A+sin²B+sin²C.

The following inter – industry transactions table was constructed for an economy of the year 2016

Industry 1 2 Final consumption Total output

1 500 1,600 400 2,500

2 1,750 1,600 4,650 8,000

Labours 250 4,800 - -

Construct technology co-efficient matrix showing direct requirements. Does a solution exist for this system.

Without expanding show that \(\Delta =\left| \begin{matrix} { cosec }^{ 2 }\theta & { cot }^{ 2 }\theta & 1 \\ { cot }^{ 2 }\theta & { cosec }^{ 2 }\theta & -1 \\ 42 & 40 & 2 \end{matrix} \right| =0\)

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