Let M - -1 -2- and N - - 2 1 -1 2 - -Dotes NM exist - Give reasons-

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Byju's Answer

Standard XII

Mathematics

Multiplication of Matrices

Let M = [1 -2...

Question

Let M = [1 -2] and N = $[\begin{matrix} 2 & 1 - 1 & 2 \end{matrix}] .$
Dotes NM exist ? Give reasons.

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Solution

$N M = {[\begin{matrix} 2 & 1 - 1 & 2 \end{matrix}]}_{2 \times 2} {[1 - 2]}_{1 \times 2}$
In order for matrix multiplication to be defined, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
Since $2 \neq 1$
$N M$ does not exist.

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Similar questions

Q. Let M = [1 -2] and N =

[\begin{matrix} 2 & 1 - 1 & 2 \end{matrix}] .

show that MN exists and write its order.

Q. Let M = [1 -2] and N =

[\begin{matrix} 2 & 1 - 1 & 2 \end{matrix}] .

Find MN.

Q. Assertion :Let

n, m \in N

and

n \geq m

Reason:

^{n} C_{m} + 2^{n - 1} C_{m} + 3^{n - 2} C_{m} + . . . +^{m} C_{m} =^{n + 1} C_{m + 1}

Q. Assertion :nm is not same as mN. Reason: 1 nm

=

^{- 9}

m and 1mN

=

^{- 3}

Explain, giving reasons, which of the following sets of quantum numbers are not possible.
a) n = 0 l = 0 ml = 0 $m, = + \frac{1}{2}$
b) n = 1 l = 0 ml = 0 $m, = - \frac{1}{2}$
c) n = 1 l = 1 ml = 0 $m, = + \frac{1}{2}$
d) n = 2 l = 1 ml = 0 $m, = - \frac{1}{2}$
e) n = 3 l = 3 ml = – 3 $m, = + \frac{1}{2}$
f) n = 3 l = 1 ml = 0 $m, = + \frac{1}{2}$

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Let M = [1 -2] and N = [21−12].Dotes NM exist ? Give reasons.

NM=[21−12]2×2[1−2]1×2In order for matrix multiplication to be defined, the number of columns in the first matrix must be equal to the number of rows in the second matrix.Since 2≠1NM does not exist.

Let M = [1 -2] and N = $[\begin{matrix} 2 & 1 - 1 & 2 \end{matrix}] .$
Dotes NM exist ? Give reasons.

$N M = {[\begin{matrix} 2 & 1 - 1 & 2 \end{matrix}]}_{2 \times 2} {[1 - 2]}_{1 \times 2}$
In order for matrix multiplication to be defined, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
Since $2 \neq 1$
$N M$ does not exist.