A is a 3 × 3 matrix where its first row is (1 0 0) , second row is (2 1 0) and third row is (3 2 1). P, Q and R are column matrices such that AP = (1 0 0)T, AQ = (2 3 0)T and AR = (0 0 1)T . If P, Q and R are three columns of matrix U , then | U| =

Question

A is a 3 × 3 matrix where its first row is (1 0 0) , second row is (2 1 0) and third row is (3 2 1). P, Q and R are column matrices such that AP = (1 0 0)T, AQ = (2 3 0)T and AR = (0 0 1)T . If P, Q and R are three columns of matrix U , then | U| =  (A)  0  (B)  1  (C)  3  (D)  9

Tardigrade Admin · Accepted Answer

We have, A=[ beginmatrix1&0&0 2&1&0 3&2&1 endmatrix] Let P=[ beginmatrixx1 y1 z1 endmatrix], Q=[ beginmatrixx2 y2 z2 endmatrix] and R=[ beginmatrixx3 y3 z3 endmatrix] Now, AP=[ beginmatrixx1 2x1+y1 3x1+2y1 +z1 endmatrix]=[ beginmatrix1 0 0 endmatrix] ⇒ x1=1, y1=-2 and z1=1 Again, AQ=[ beginmatrixx2 2x2+y2 3x2 2y2 +z2 endmatrix]=[ beginmatrix2 3 0 endmatrix] ⇒ x2=2, y2=-1 and z2=-4 ∴ AR=[ beginmatrixx3 2x3 +y3 3x3+2v3 +z3 endmatrix]=[ beginmatrix0 0 1 endmatrix] ⇒ x3=0, y3=0 and z3=1 So, U=[ beginmatrix1&2&0 -2&-1&0 1&-4&1 endmatrix] |U|=1(-1+4) =3

Q. $A$ is a $3 \times 3$ matrix where its first row is $(100)$ , second row is $(210)$ and third row is $(321) . P, Q$ and $R$ are column matrices such that $A P = (100)^{T}, A Q = (230)^{T}$ and $A R = (001)^{T}$ . If $P, Q$ and $R$ are three columns of matrix $U$ , then $∣ U ∣ =$

$0$

$1$

$3$

$9$

Q. A is a 3×3 matrix where its first row is (100) , second row is (210) and third row is (321).P,Q and R are column matrices such that AP=(100)T,AQ=(230)T and AR=(001)T . If P,Q and R are three columns of matrix U , then ∣U∣=

0

1

3

9

Q. $A$ is a $3 \times 3$ matrix where its first row is $(100)$ , second row is $(210)$ and third row is $(321) . P, Q$ and $R$ are column matrices such that $A P = (100)^{T}, A Q = (230)^{T}$ and $A R = (001)^{T}$ . If $P, Q$ and $R$ are three columns of matrix $U$ , then $∣ U ∣ =$

$0$

$1$

$3$

$9$