Compute the product using​ (a) the definition where Ax is the linear combination of the columns of A using the corresponding entries in x as​ weights, and​ (b) the​ row-vector rule for computing Ax. If a product is​ undefined, explain why.

When the number of rows or number of columns in the given matrix does not match the number of entries in the vector x.

When the number of columns in A the number of rows in B.

The matrix-vector is not defined.

Step-by-step explanation:

For example:-

Step 1:

Let's assume

3x2                 &       3x1

Since matrix multiplication of matric A and matrix B is only possible,

When the number of columns in A = Number of rows in B.

Step 2:

Let's A as m x n; Here m = rows and n=columns

B as p x q; Here p = rows and q=columns.

When n p, the matrix-vector is not defined.

That is matrix multiplication Ax is not possible.

Hence the matrix is not defined.

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.