PPSC Mathematics lecturer past papers with answers

For any non-singular matrices A and B it is true that:

A). (𝐴𝐵)⁻¹ = 𝐵⁻¹𝐴⁻¹

B). (𝐴𝐵)^𝑡 = 𝐵^𝑡𝐴^𝑡

C). 𝐴𝐵 ≠ 𝐵𝐴

D). all of these

Solution set of the equation 𝒙^𝟐 − 𝟒𝒙 + 𝟒 = 𝟎 is:

Which of the following Sets is a field:

In echelon form of matrix, the first non zero entry is called:

In a homogeneous system of linear equations , the solution (0,0,0) is:

A square matrix 𝑨 = [𝒂_𝒊𝒋] for which 𝒂_𝒊𝒋 = 𝟎, 𝒊 < 𝑗 then A is called:

A square matrix 𝑨 = [𝒂_𝒊𝒋] for which 𝒂_𝒊𝒋 = 𝟎, 𝒊 > 𝑗 then A is called:

The equation 𝒂𝒙^𝟐 + 𝒃𝒙 + 𝒄 = 𝟎 will be quadratic if:

For a non-singular matrix it is true that :

A). (𝐴⁻¹)⁻¹ = 𝐴

B). (𝐴^𝑡)^𝑡 = 𝐴

C). 𝐴̿ = 𝐴

D). all of these

If 𝑨𝑿 = 𝑶 then 𝑿 =

 If a square matrix 𝑨 has two identical rows or two identical columns then:

If all entries of a square matrix of order 𝟑 is multiplied by 𝒌, then value of |𝒌𝑨| is equal to:

A). 𝑘|𝐴|

B). 𝑘²|𝐴|

C). 𝑘³|𝐴|

D). |𝐴|

The main diagonal elements of a skew hermitian matrix must be:

The value of 𝝀 for which the system 𝒙 + 𝟐𝒚 = 𝟒; 𝟐𝒙 + 𝝀𝒚 = −𝟑 does not possess the unique solution

How many techniques to solve quadratic equations:

 If A is symmetric (Skew symmetric), then 𝑨^𝟐 must be

Which of the following Sets is not a field:

For any matrix A , it is always true that:

a). 𝐴 = 𝐴^𝑡

b). – 𝐴 = 𝐴̅

c). |𝐴| = |𝐴^𝑡|

d). 𝐴⁻¹ = ^1/A

If the system of linear equations have no solution at all, then it is called a/an:

To convert 𝟒^𝟏+𝒙 + 𝟒^𝟏−𝒙 = 𝟏𝟎 into quadratic , the substitution is:

A). 𝑦 = 𝑥^1−𝑥

B). 𝑦 = 4^1+𝑥

C). 𝑦 = 4^𝑥

D). 𝑦 = 4^−𝑥

If a matrix is in triangular form, then its determinant is product of the entries of its:

To convert 𝒂𝒙^𝟐𝒏 + 𝒃𝒙^𝒏 + 𝒄 = 𝟎(𝒂 ≠ 𝟎) into quadratic form , the correct substitution is:

A). 𝑦 = 𝑥^𝑛

B). 𝑥 = 𝑦^𝑛

C). 𝑦 = 𝑥^−𝑛

D). 𝑦 = ^1/𝑥

(𝑨^−𝟏)𝒕 =

 The solution of a quadratic equation are called:

 The equation in which variable occurs in exponent , called: