# Jambmaths

Maths Question
Question 21

A matrix $P=\left( \begin{matrix} a & b \\ c & d \\\end{matrix} \right)$is such that PT = -P. PT is the transpose of P. If b = 1, then P is

Question 22

Find the value of t for which the determinant of   the matrix$\left( \begin{matrix} t-4 & 0 & 0 \\ -1 & t+1 & 1 \\ 3 & 4 & t-2 \\\end{matrix} \right)$is zero

Question 12

If $P=\left( \begin{matrix} 3 & -2 & 4 \\ 5 & 0 & 6 \\ 7 & 5 & -1 \\\end{matrix} \right)$ then –2p is

Question 13

Given the matrix $k=\left( \begin{matrix} 2 & 1 \\ 3 & 4 \\\end{matrix} \right)$ the matrix k2 +k +1 is , where I is the 2× 2 identity matrix

Question 16

Evaluate $\left| \begin{matrix} -1 & -1 & -1 \\ 3 & 1 & -1 \\ 1 & 2 & 1 \\\end{matrix} \right|$

Question 16

If $P=\left( \begin{matrix} 2 & 1 \\ -3 & 0 \\\end{matrix} \right)$ and I is a 2 × 2 unit matrix. Evaluate ${{p}^{2}}-2p+4I$

Question 24

If $N=\left( \begin{matrix} 3 & 5 & -4 \\ 6 & -3 & -5 \\ -2 & 2 & 1 \\\end{matrix} \right)$, find $\left| N \right|$

Question 14

$\left| \begin{matrix} -x & 2 \\ 4x & 1 \\\end{matrix} \right|=\left| \begin{matrix} 3 & 3x \\ 4 & -5 \\\end{matrix} \right|$, find the value of x

Question 21

A matrix P has an inverse ${{P}^{-1}}=\left( \begin{matrix} 1 & -3 \\ 0 & 1 \\\end{matrix} \right)$find P

Question 30

The inverse of the matrix $\left[ \begin{matrix} 2 & 1 \\ 1 & 1 \\\end{matrix} \right]$is

Question 37

if $P=\left( \begin{matrix} 1 & 0 & -1 \\ 3 & 4 & 5 \\ -1 & 0 & 1 \\\end{matrix} \right)$, then $\left| P \right|$ is

Question 48

If $P=\left( \begin{matrix} 1 & 3 & 2 \\ 4 & 5 & -1 \\ -3 & 2 & 0 \\\end{matrix} \right)$find the determinant of matrix P

Question 50

If M and N are two matrices defined by  $M=\left( \begin{matrix} 1 & 3 & 2 \\ 4 & 5 & -1 \\ -3 & 2 & 0 \\\end{matrix} \right)$and$\left( \begin{matrix} 1 & -2 & 3 \\ 4 & -1 & 5 \\ 2 & -3 & -1 \\\end{matrix} \right)$,evaluate 2M – 3N

Question 31

If $x=\left[ \begin{matrix} 1 & 0 & 1 \\ 2 & -1 & 0 \\ -1 & 0 & 1 \\\end{matrix} \right]$ and $y=\left[ \begin{matrix} -1 & 1 & 2 \\ 0 & -1 & -1 \\ 2 & -1 & -1 \\\end{matrix} \right]$find 2xy

Question 37

Find p, q for which\left( \begin{matrix} 2p & 8 \\ 3 & -5q \\\end{matrix} \right)\left( \begin{align} & 1 \\ & 2 \\\end{align} \right)=\left( \begin{align} & 24 \\ & -17 \\\end{align} \right)

Question 22

$\left( \begin{matrix} 3 & -2 \\ -7 & 5 \\\end{matrix} \right)+2\left( \begin{matrix} -2 & 4 \\ 3 & -1 \\\end{matrix} \right)$

Question 23

If f(x) = 3x – 2, P =$\left( \begin{matrix} 2 & 1 \\ -1 & 0 \\\end{matrix} \right)$and I is 2 × 2, identity matrix, evaluate f(p)

Question 23

Find the value of x and y respectively if $\left( \begin{matrix} 1 & 0 \\ -1 & -1 \\ 2 & 2 \\\end{matrix} \right)+\left( \begin{matrix} x & 1 \\ -1 & 0 \\ y & -2 \\\end{matrix} \right)=\left( \begin{matrix} -2 & 1 \\ -2 & -1 \\ -3 & 0 \\\end{matrix} \right)$

Question 24

If $\left( \begin{matrix} -2 & 1 \\ 2 & 3 \\\end{matrix} \right)\left( \begin{matrix} p & q \\ r & s \\\end{matrix} \right)=\left( \begin{matrix} 1 & 0 \\ 0 & 1 \\\end{matrix} \right),$what is the value of r

Question 22

If $Q=\left( \begin{matrix} 9 & -2 \\ -7 & 4 \\\end{matrix} \right),\text{then }\left| Q \right|\text{is}$

Question 23

If $\left( \begin{matrix} x+3 & x+2 \\ x+1 & x-1 \\\end{matrix} \right)$, evaluate x if $\left| P \right|=-10$

Question 25

If $\left| \begin{matrix} x & 3 \\ 2 & 7 \\\end{matrix} \right|=15$find the value of x

Question 26

Evaluate $\left| \begin{matrix} 2 & 0 & 5 \\ 4 & 6 & 3 \\ 8 & 9 & 1 \\\end{matrix} \right|$

Question 27

If P = $\left( \begin{matrix} 2 & -3 \\ 1 & 1 \\\end{matrix} \right)$what is P -1

Question 24

If $\left| \begin{matrix} 2 & 3 \\ 5 & 3x \\\end{matrix} \right|=\left| \begin{matrix} 4 & 1 \\ 3 & 2x \\\end{matrix} \right|$ find the value of x

Question 25

Evaluate $\left| \begin{matrix} 4 & 2 & -1 \\ 2 & 3 & -1 \\ -1 & 1 & 3 \\\end{matrix} \right|$

Question 26

The inverse of matrix N =$\left( \begin{matrix} 2 & 3 \\ 1 & 4 \\\end{matrix} \right)$ is

Question 23

if $\left| \begin{matrix} 5 & 3 \\ x & 2 \\\end{matrix} \right|=\left| \begin{matrix} 3 & 5 \\ 4 & 5 \\\end{matrix} \right|$, find the value of x

Question 24

Given that I3 is a unit matrix of order 3 find $\left| {{I}_{3}} \right|$

Question 22

\begin{align} & \text{If }P=\left[ \begin{matrix} 5 & 3 \\ 2 & 1 \\\end{matrix} \right]\text{ and }Q=\left[ \begin{matrix} 4 & 2 \\ 3 & 5 \\\end{matrix} \right],\text{ find }2P+Q \\ & (A)\text{ }\left[ \begin{matrix} 8 & 14 \\ 7 & 7 \\\end{matrix} \right] \\ & (B)\text{ }\left[ \begin{matrix} 7 & 7 \\ 14 & 8 \\\end{matrix} \right] \\ & (C)\text{ }\left[ \begin{matrix} 14 & 8 \\ 7 & 7 \\\end{matrix} \right] \\ & (D)\text{ }\left[ \begin{matrix} 7 & 7 \\ 8 & 14 \\\end{matrix} \right] \\\end{align}

Question 23

\begin{align} & \text{Find the inverse of }\left[ \begin{matrix} 5 & 3 \\ 6 & 4 \\\end{matrix} \right] \\ & (A)\left[ \begin{matrix} 2 & \tfrac{3}{2} \\ -3 & \tfrac{5}{2} \\\end{matrix} \right] \\ & (B)\left[ \begin{matrix} 2 & -\tfrac{3}{2} \\ -3 & -\tfrac{5}{2} \\\end{matrix} \right] \\ & (C)\left[ \begin{matrix} 2 & -\tfrac{3}{2} \\ -3 & \tfrac{5}{2} \\\end{matrix} \right] \\ & (D)\,\left[ \begin{matrix} 2 & \tfrac{3}{2} \\ -3 & -\tfrac{5}{2} \\\end{matrix} \right] \\\end{align}

Question 22

Find y, ifleft( \begin{matrix} 5 & -6 \\ 2 & 7 \\\end{matrix} \right)\left( \begin{align} & x \\ & y \\\end{align} \right)=\left( \begin{align} & 7 \\ & -11 \\\end{align} \right)

Question 23

If $\left| \begin{matrix} -x & 12 \\ -1 & 4 \\\end{matrix} \right|=-12$, find x

Question 24

Find the value of $\left| \begin{matrix} 0 & 3 & 2 \\ 1 & 7 & 8 \\ 0 & 5 & 2 \\\end{matrix} \right|$

Question 17

If $P=\left( \begin{matrix} 2 & 3 \\ 4 & 5 \\\end{matrix} \right)$ and $Q=\left( \begin{matrix} 4 & 2 \\ 3 & 3 \\\end{matrix} \right)$

Question 30

Find the value of $\left| \begin{matrix} 0 & 3 & 2 \\ 1 & 7 & 8 \\ 0 & 5 & 4 \\\end{matrix} \right|$

Question 23

Find the determinant of $\left( \begin{matrix} 1 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 1 & 2 \\\end{matrix} \right)$

Question 28

If $Q=\left( \begin{matrix} 3 & -2 & 1 \\ -2 & 1 & -1 \\ 1 & -3 & 2 \\\end{matrix} \right)$ then –3Q is