# t test and F test are equivalent under single restriction case

In Classic linear regression model, under the single restriction

$$y=X\beta +u$$ $$H_0: \beta_j=0$$

If I apply t test, then the t statistic is derived as follows

$$\frac{b_j-\beta_j}{s\sqrt{a_{jj}}}$$

Where $$b_j$$ is OLS estimate of beta. And $$s\sqrt{a_{jj}}$$ is the estimated standard error of $$b_j$$.

I can use F statistic

And F statistic is as follows:

$$\frac{e_R’e_R - e’e}{e’e}.(n-k)/k_2$$

where $$y= X_1\beta_1+X_2\beta_2+u$$

I write the same regression in the partitioned form.

My question is that how I can show these two are equivalent for single restriction?