Question

In: Math

10. Assume k is a scalar and A is a m × n matrix. Show that...

10. Assume k is a scalar and A is a m × n matrix. Show that if kA = 0 then either k = 0 or A = 0m x n

Expert Solution

Here, k is a scalar and A is a mxn matrix.

Then, A = is a mxn matrix.

Now, kA = k =

Given kA = O

i.e., =

i.e., ka_ij = 0, where 1 i m and 1 j n.

which implies either k = 0 or a_ij = 0.

[Since we know that product of two numbers is 0 implies that one of them must be 0]

Now, a_ij = 0 for 1 i m, 1 j n implies =

i.e., A = .

Therefore, if kA = 0 then either k = 0 or A = 0_mxn.

milcah answered 2 years ago

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