Question

If [1 2 3] B = [34], then the order of the matrix B is
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Answer 1

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TO DETERMINE

The order of the matrix B when

[ 1 2 3 ] B = [ 3 4 ]

CONCEPT TO BE IMPLEMENTED

Two matrices A and B can be multiplied only when the number of columns in the First matrix is equal to the number of rows in the Second matrix

CALCULATION

Let

A = [ 1 2 3 ]

C = [ 3 4 ]

Now the order of the matrix A is 1 × 3

and the order of the matrix C is 1 × 2

Let the order of B is m × n

Since multiplication A and B are possible

So

Number of columns in A = Number of rows in B

$\implies \sf{ 3 = m\: }$

$\implies \sf{ m = 3\: }$

Again The order of AB is 3 × n

Since AB = C

So

Number of columns of AB = Number of columns of C

$\implies \sf{ n \: = 2}$

Hence the order of B is 3 × 2

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LEARN MORE FROM BRAINLY

For a square matrix A and a non-singular matrix B of the same order, the value of det(B^-1 AB) is

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Answer 2

Step-by-step explanation:

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Solution

TO DETERMINE

The order of the matrix B when

[ 1 2 3 ] B = [ 3 4 ]

CONCEPT TO BE IMPLEMENTED

Two matrices A and B can be multiplied only when the number of columns in the First matrix is equal to the number of rows in the Second matrix

CALCULATION

Let

A = [ 1 2 3 ]

C = [ 3 4 ]

Now the order of the matrix A is 1 × 3

and the order of the matrix C is 1 × 2

Let the order of B is m × n

Since multiplication A and B are possible

So

Number of columns in A = Number of rows in B

\implies \sf{ 3 = m\: }⟹3=m

\implies \sf{ m = 3\: }⟹m=3

Again The order of AB is 3 × n

Since AB = C

So

Number of columns of AB = Number of columns of C

\implies \sf{ n \: = 2}⟹n=2

Hence the order of B is 3 × 2

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

For a square matrix A and a non-singular matrix B of the same order, the value of det(B^-1 AB) is

https://brainly.in/question/23783093